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Maths-

General

Easy

Question

Find the solution of the system of equations.
$y equals 2 x squared plus 5 x minus 30$
y = 2x + 5

hint Hint:

A graph is a geometrical representation of an equation or an expression. It can be used to solve by equating them to zero.
We are asked to solve the set of equation.

The correct answer is: We are asked to solve the set of equation.

Step 1 of 3:
The LHS of the set has the same value. Thus, equate the RHS of the set of equation to get the simplified equation.
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 x squared plus 5 x minus 30 equals 2 x plus 5 space space space space space space end cell row cell 2 x squared plus 5 x minus 2 x minus 30 minus 5 equals 0 end cell row cell 2 x squared plus 3 x minus 35 equals 0 space space space space space space space space space space space space space space end cell end table$
Step 2 of 3:
Solve the simplified equation.
Find two numbers such that their product are : ab = 2(35) = 70 and the sum is a + b =3.
Here, the numbers are; $a equals 10 straight & b equals negative 7$
Thus, we have the solution as:
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 x squared plus 3 x minus 35 equals 0 space space space space space space space space space end cell row cell 2 x squared plus 10 x minus 7 x minus 35 equals 0 end cell row cell 2 x left parenthesis x plus 5 right parenthesis minus 7 left parenthesis x plus 5 right parenthesis equals 0 end cell row cell left parenthesis 2 x minus 7 right parenthesis left parenthesis x plus 5 right parenthesis equals 0 space space space space space space space space end cell row space end table$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 x minus 7 equals 0 end cell row cell x equals 7 over 2 space space space space space space end cell row cell left parenthesis x plus 5 right parenthesis equals 0 end cell row cell x equals negative 5 space space space space space end cell end table$
Step 3 of
Substitute the values of in any of the equation to get the values of y;
When x = -5,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x plus 5 space space space space space space end cell row cell y equals 2 left parenthesis negative 5 right parenthesis plus 5 end cell row cell y equals negative 10 plus 5 space space space end cell row cell y equals negative 5 space space space space space space space space space space space end cell end table$
when $x equals 7 over 2$ ,
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 2 x plus 5 space space space space space end cell row cell y equals 2 open parentheses 7 over 2 close parentheses plus 5 end cell row cell y equals 7 plus 5 space space space space space space space space end cell row cell y equals 12 space space space space space space space space space space space space end cell end table$
Thus, the required solutions of the set of equation are (-5, -5) and (7/2,12).

A set of equations can also be solved by graphing them. Find the points where they intersect each other.

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