Question
Solve: 3x + y = 8; 5x + y = 10 by using elimination method.
Hint:
find x by eliminating y and find y by substituting x in the equations .
The correct answer is: x = 1 ; y = 5
Ans :- x = 1 ; y = 5
Explanation :-
— eq 1
— eq 2
Step 1 :- find x by eliminating y
Eliminating x by subtracting eq 2- eq1 then
![left parenthesis 5 x plus y right parenthesis minus left parenthesis 3 x plus y right parenthesis equals 10 minus 8](data:image/png;base64,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)
![not stretchy rightwards double arrow 5 x minus 3 x plus y minus y equals 2](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAPCAYAAAAVv3adAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAndJREFUeNrtmcFLG0EUxpcgQUQKJYQcPAihhyIigngQKUEQERGRQCgiUsR/IBRvRXoQQXoIHrxJDyKlUIpIkSCUEqSUIhSR4EEKIv4DHjxIkML2G/gKy7LJ7iTzJpruBz/ITnb3vXnzZuZN4jgychvQTk2AMrgDNfAbbIGUE8ukxsFncAvuwRlYtGHYfaABqYA8SHrahsFRnCtGdQwWQC+vB8APtv2XiVdPt3EcxNUPqs0+vAqeGA74CtgMaF/nd9LKggshv6LG4T14GdBeBBsG+2rLTj3Vmn3wDbjmHm5ypp+CjOd6GWwLByFDO6rOmxHyK2ocXoF3vrYe+may/tS140Ygqsa43TZ1MPCiZkiiwTvuuYWpYv61Z78P0jQo8fMk+CZcBngpCvoVdWBU4n/ytb0Fa4b7bsuOX93gJMKCFWnJVkH9EHJfFxhhx9R29rzBvV9BjieglGbyNDMTn4J5BiTXZr/Ue88912lwyQFrpx0TUnE+AFOOgeC5rH8SGg5M8bRTT0WukkOWi95eJp+EXzpb0Z3ncylkJW5FOnZaneBZJt2zVp2OWuPpFpf/fvcp2ThyW/RLJ/G+c6CyXIUSQn21ZUftbjusIVvWakit1kiD7GjQrPhCB9W7fzl2f9AdYnEt4ZdO4u2COZYvS4L9tWEnw1qyy/YKss9TTIJMM+nyvvvSPHx4B3QW7An5pbb6AgOi/FL/ZFzxtCfhl07iFVk7V4XHxoadw5B6XkwFriJ/wA2zf9R3T5IJ2hfw/Ecmq2m9YFBqpMKEardfDg86LlcjSdmw81D/Mo0VIJUIPzvITqxHojLLk06xE+sRaJAlQKfYCdVfWL3g/fU5iL4AAADddEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjFEMjs8L21vPjxtbj41PC9tbj48bWk+eDwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bW4+MzwvbW4+PG1pPng8L21pPjxtbz4rPC9tbz48bWk+eTwvbWk+PG1vPiYjeDIyMTI7PC9tbz48bWk+eTwvbWk+PG1vPj08L21vPjxtbj4yPC9tbj48L21hdGg+HWkHKAAAAABJRU5ErkJggg==)
![not stretchy rightwards double arrow 2 x equals 2](data:image/png;base64,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)
![rightwards double arrow x equals space 1](data:image/png;base64,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)
Step 2 :- substitute value of x and find y
![not stretchy rightwards double arrow 5 x plus y equals 10](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGgAAAAPCAYAAAAI7YpDAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAgdJREFUeNpjYKAN+I8HjySgBsS1QHwBjxo+IJ4GxCeheCZUjKZgpEUELrAYiNMIhMdeIPZD4vtAxYZVBA32BIHLfaFAPAmL+AQgjiTHohIisx8pAZYMxB1YxJuhctSMoLlAHI5FvACIWwcggtYAsRsWcUeoHMmgGogfArE1lVP0OSAWR+InAvEUGuSgeCDuQhPjAuJbQCxMYl1KSp2KS907IGbDIg4Se0lOBY+MQSmOCY8Zv4D4ExBvA+IiIObB4wEPIO6Dsl3IKIOJDSgvIF6FJlYPrcgHooj7g0fPL0osnAu1dCkBdSxAbAwNgBtArIFH7W4gtoe2eIQpaCXiS9kgc68g8UWB+C4QcwzCCPpBaQ7qwJODsAFQWXsQj3wBNNXo0biR8A2J3Qe1l9oJgVj3vcRRxHHgK+KoUQeRmiqsoZViH5mtF1Ii6DAQK0HxXRITGS0aCR44EjNZjYQSAnUJPqADDRB0AAqoTdDKGmT2GSKKOEoiaCG03wEqnmMHuJkdBMSzsYjPJ7eZTSxYB8SW0NTJBE0ld6EOYkCrA7ahRYgPtINHqwgqgNahlwZJP20/1E0s0OKumkBVQBUQCm26/oE2JUEtJ1MsTUlQREpj0b8cR9anBgiABpgfnSKGUJ0lCE0wP6D140wKSqlhAUARc3x0FGrwgm3Q4ncUDEIAaqhsGUoOBgBAhaePp01w3QAAAJ50RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8gc3RyZXRjaHk9ImZhbHNlIj4mI3gyMUQyOzwvbW8+PG1uPjU8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1pPnk8L21pPjxtbz49PC9tbz48bW4+MTA8L21uPjwvbWF0aD7vhoXkAAAAAElFTkSuQmCC)
![not stretchy rightwards double arrow 5 left parenthesis 1 right parenthesis plus y equals 10](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHEAAAARCAYAAADqikOKAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAAi9JREFUeNpjYBgcIAuIO0hQ3wHVMwoGCdAD4uNk6DsK1TsKaAT+48HYIsMAi7gaENcC8QUcdhgD8eFhEFaE/AkCfEA8DYhPQvFMqBjNI5EYYACNRGxgMRCnETDrMDQyhzIgxp97gdgPie8DFRsUkdgFxDkUmJVHQl36f5BHJi73hQLxJCziE4A4khyLSojMxsQG2A4gtqXALEsSUiSxbpoLxOFYxAuAuHUAInENELthEXeEypEMqoH4IRBbUynAPgExGwVmsUHNoGYkxkNLCGTABcS3gFiYxPr/Pwn24lL3DkcYgcRektMoQcagVMmEx4xf0ADeBsRFQMyDRd0fKgT+LypHohcQr0ITq4c2PgaiOP1DBb/jLHJAli4loI4F2vAABcANINagYySSm0NAue0KEl8UiO8CMccgjMQflObEDjw5ERsAlesHh0BxCgLfkNh90PqQgcqJhVj3vcQRRhz4ilNq1InEppzdFNavtGjYwLouSlB8l8TESouGjQeOTEFWw6YER91GDNCBBgg1uxg5WBoh1IjEhdB+Gai6iB3gLkYQEM/GIj6f3C4GsWAdNJcwQbEHNAKDSOjsExP4pHT2SYnEAmi9f2kQ9BNBYD/UTSzQorUaS9VEdRAKbZL/gTaRQa09UxxqQeOmekTWNciAlsNuAVD7/OgUeYTqUEFoovoBra9nUlAi0gQMxgFwPzLdNKJBBgNpU1GgejCNhu7ZBq0ORsEQBaAG2Jah5GAAsyzHnkddQSoAAACydEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjFEMjs8L21vPjxtbj41PC9tbj48bW8+KDwvbW8+PG1uPjE8L21uPjxtbz4pPC9tbz48bW8+KzwvbW8+PG1pPnk8L21pPjxtbz49PC9tbz48bW4+MTA8L21uPjwvbWF0aD7oEYRFAAAAAElFTkSuQmCC)
![not stretchy rightwards double arrow y equals 10 minus 5](data:image/png;base64,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)
![not stretchy rightwards double arrow y equals 5](data:image/png;base64,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)
![therefore space y space equals space 5](data:image/png;base64,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)
and y = 5 is the solution of the given pair of equations.
Related Questions to study
Solve
and
by using elimination method.
Solve
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by using elimination method.
Solve by using elimination method: ![fraction numerator 2 x minus 3 over denominator 4 end fraction minus fraction numerator 2 x minus 1 over denominator 3 end fraction equals 1](data:image/png;base64,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)
Solve by using elimination method: ![fraction numerator 2 x minus 3 over denominator 4 end fraction minus fraction numerator 2 x minus 1 over denominator 3 end fraction equals 1](data:image/png;base64,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)
Solve by using elimination method.
.
Solve by using elimination method.
.
Solve the following equation by balancing on both sides: b) 6n+7= 3n+25
Solve the following equation by balancing on both sides: b) 6n+7= 3n+25
Solve the following equation by balancing on both sides: a) 5m+9 = 4m + 23
Solve the following equation by balancing on both sides: a) 5m+9 = 4m + 23
Solve: ![fraction numerator 7 x plus 1 over denominator 4 end fraction equals 2 x minus 1](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHkAAAAjCAYAAACw76XYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAfVJREFUeNrtmj9LA0EUxA8RkWAjIhYWgRBELMRWLEQQSZHCxiJYiSAWFn4BKxsrKxuxtBBERERsJIVIioCIpBC/gq2V2MRZ8gJB7p+5XW93Mz8YCJdNcjC3b9/OJgjCaScob2agA+g1INrZgM4suI9zaMeSB84rpqAnaNTAd7f/+XMkgltoIeT6NnQUcv1Q3qPJjrAra2AULzLTu2xBJ5zJ7lCEmtBwzJgKdCyvV6E6y7VbPEIrKcY9QMvS8U6kMEdHB0+TNXXT9ynH7kPf0DwbL3cYgt4jmq3fLEFXUrJrNNkd1qVUJ1GSzrsAjUHPKco1TbaEC+mS45iUct5ralXCCprsAB/QeMz7I9A1NB3xgFQM3lseUWt3SfqU3kM1mJsW+cWoV9MuoyZLkmIOavTZg5iAUa/BDKFl2T3RZAN8hVzTEfXSZM3reb/r+6KU7DCyRr002QLUaVxTGrIwska9RkxueyaTqF3HDbSWMI5Rr6PluiQGl1P8Vpaol+U6J2aDzj9jCn/YV/cb9dLkHFBN1GUQf+TaO9uzRr00OQfuZCYnoSvqpcmWreVdBi3qjaTKp81v1Pr0RpP95jToxHo02VPUlqLO5sBfVEOiTmuKNNlf1InMHtt8f1GRXoN7Ob9RJzVlmjy4IQLN9tx4QpMJTSap+QHqb+TxLDkRtAAAAMZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1uPjc8L21uPjxtaT54PC9taT48bW8+KzwvbW8+PG1uPjE8L21uPjwvbXJvdz48bW4+NDwvbW4+PC9tZnJhYz48bW8+PTwvbW8+PG1uPjI8L21uPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtbj4xPC9tbj48L21hdGg+eKjRKgAAAABJRU5ErkJggg==)
Solve: ![fraction numerator 7 x plus 1 over denominator 4 end fraction equals 2 x minus 1](data:image/png;base64,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)
![table attributes columnspacing 1em end attributes row cell left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 40 end cell row cell y equals negative 2 x plus 4 end cell end table](data:image/png;base64,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)
Which of the following could be the x-coordinate of a solution to the system of equations above?
Note:
If we had to find the y-coordinate of the system of equations, then we put this value of x in the equation to get the value of y. Here, we got a quadratic equation of x, which did not have any term containing x, so it was easier to solve. If the quadratic equation was of the form
, then we would use the quadratic formula
to solve the equation.
![table attributes columnspacing 1em end attributes row cell left parenthesis x plus 2 right parenthesis squared plus left parenthesis y minus 3 right parenthesis squared equals 40 end cell row cell y equals negative 2 x plus 4 end cell end table](data:image/png;base64,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)
Which of the following could be the x-coordinate of a solution to the system of equations above?
Note:
If we had to find the y-coordinate of the system of equations, then we put this value of x in the equation to get the value of y. Here, we got a quadratic equation of x, which did not have any term containing x, so it was easier to solve. If the quadratic equation was of the form
, then we would use the quadratic formula
to solve the equation.
Solve the equation and check your result 6(3m + 2) – 2(6m – 1) = 3(m – 8) – 6(7m – 6) +9m
Solve the equation and check your result 6(3m + 2) – 2(6m – 1) = 3(m – 8) – 6(7m – 6) +9m
Solve and check your answer: 3x – 2(2x – 5) = 2(x + 3) – 8
Solve and check your answer: 3x – 2(2x – 5) = 2(x + 3) – 8
Solve: 16 = 4 + 3(x + 2)
Solve: 16 = 4 + 3(x + 2)
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)
The graph of the function f is shown in the xy-plane above, where y =f
. Which of the following functions could define f ?
Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.
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)
The graph of the function f is shown in the xy-plane above, where y =f
. Which of the following functions could define f ?
Note:
We need to know properties about factors, multiplicity, leading co-efficients and turning points to find out the function from a graph.
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?
At a restaurant, n cups of tea are made by adding t tea bags to hot water. If t n = +2, how many additional tea bags are needed to make each additional cup of tea?
f(x) =2x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?
f(x) =2x +1
The function f is defined by the equation above. Which of the following is the graph of y = - f(x)in the xy-plane?
![2000 minus 61 k equals 48](data:image/png;base64,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)
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.
![2000 minus 61 k equals 48](data:image/png;base64,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)
In 1962, the population of a bird species was 2,000. The population k years after 1962 were 48, and k satisfies the equation above. Which of the following is the best interpretation of the number 61 in this
context?
Note:
This question could also be solved by eliminating the options. Option A is wrong as the population k years after 1962 is 48, not 61. Option B is wrong because we find the value of k to be 32. Option C is wrong because the difference between the population in 1962 and the population k years after 1962 is given by 2000-48=1952.