Maths-
General
Easy
Question
Solve Each system : Explain your choice of Solution method
2X - 3Y = 14
5X + 4Y = 12
Hint:
Choose the correct method of solution and perform any arithmetic operation
and then find.
The correct answer is: x=107/23 and y=(-36)/23
Complete step by step solution:
We can use the method of elimination of the system of equations.
Let 2x -3y = 14…(i)
and 5x + 4y = 12….(ii)
On multiplying (i) with 5, we get 5(2x - 3y = 14)
⇒10x - 15y = 70…(iii)
On multiplying (ii) with 2, we get 2( 5x + 4y = 12)
⇒10x + 8y = 24…(iv)
Now, we have the coefficients of x in (iii) and (iv) to be the same.
On subtracting (iii) from (iv),
we get LHS to be 10x + 8y - (10x - 15y) = 8y + 15y = 23y
and RHS to be 24 - 70 = - 36
On equating LHS and RHS, we have 23y = - 36
On substituting the value of y in (i), we get 
Hence we get 
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.
On multiplying (ii) with 2, we get 2( 5x + 4y = 12)
Now, we have the coefficients of x in (iii) and (iv) to be the same.
On subtracting (iii) from (iv),
we get LHS to be 10x + 8y - (10x - 15y) = 8y + 15y = 23y
and RHS to be 24 - 70 = - 36
On equating LHS and RHS, we have 23y = - 36
On substituting the value of y in (i), we get
Hence we get
Note: We can also solve these system of equations by making the coefficients of y
to be the same in both the equations.
Related Questions to study
Maths-
The first and the last bird are sitting 40 cm apart. Find the distance between the third and the fourth bird using the segment addition postulate.
The first and the last bird are sitting 40 cm apart. Find the distance between the third and the fourth bird using the segment addition postulate.
Maths-General
Maths-
Solve System of equations using Substitution :
Y = 2X-1
2X +3 Y = -7
Solve System of equations using Substitution :
Y = 2X-1
2X +3 Y = -7
Maths-General
Maths-
Find the distance between the coffee shop and the school.
Find the distance between the coffee shop and the school.
Maths-General
Maths-
Solve Each system : Explain your choice of Solution method
5X - 2Y = - 6
3X - 4Y = - 26
Solve Each system : Explain your choice of Solution method
5X - 2Y = - 6
3X - 4Y = - 26
Maths-General
Maths-
Solve Each system : Explain your choice of Solution method
8X - 4Y = - 4
X= Y - 4
Solve Each system : Explain your choice of Solution method
8X - 4Y = - 4
X= Y - 4
Maths-General
Maths-
Hari rides his bike from his home for 30 minutes at a fast pace. He stops to rest for 20 minutes and then continues in the same direction at a slower pace for 30 more minutes. Sketch a graph of the relationship of Hari’s distance from home over time ?
Hari rides his bike from his home for 30 minutes at a fast pace. He stops to rest for 20 minutes and then continues in the same direction at a slower pace for 30 more minutes. Sketch a graph of the relationship of Hari’s distance from home over time ?
Maths-General
Maths-
Solve Each system : Explain your choice of Solution method .
6X - 5Y= - 1
6X + 4Y= - 10
Solve Each system : Explain your choice of Solution method .
6X - 5Y= - 1
6X + 4Y= - 10
Maths-General
Maths-
Solve System of equations using Substitution :
X = Y + 6
X + Y = 10
Solve System of equations using Substitution :
X = Y + 6
X + Y = 10
Maths-General
Maths-
At a Clothing Store , 3 shirts and 8 hats costs $65.The Cost for 2 shirts and 2 Hats is $30.How much does each shirt and hat cost ?
At a Clothing Store , 3 shirts and 8 hats costs $65.The Cost for 2 shirts and 2 Hats is $30.How much does each shirt and hat cost ?
Maths-General
Maths-
Bose is practicing Javelin throws. What is the relationship between the height of the javelin and time ? What would the graph of this function look like?
H = 
g T2, where H is maximum height and T is time of the flight.
Bose is practicing Javelin throws. What is the relationship between the height of the javelin and time ? What would the graph of this function look like?
Maths-General
H = g T2, where H is maximum height and T is time of the flight.
Maths-
Nate starts a lawn – mowing business. In his business he has expenses and revenue. Nate’s expenses are the cost of the lawn mower and gas and his revenue is $25 per lawn. At What point will Nate’s revenue exceed his expenses?
Nate starts a lawn – mowing business. In his business he has expenses and revenue. Nate’s expenses are the cost of the lawn mower and gas and his revenue is $25 per lawn. At What point will Nate’s revenue exceed his expenses?
Maths-General
Maths-
Find the value of x if the vertical lines of the letter H are parallel.
Find the value of x if the vertical lines of the letter H are parallel.
Maths-General
Maths-
The midpoint of 𝑋𝑌 is M (8, 10). One endpoint is Y (1, 2). Find the coordinates of endpoint Y.
The midpoint of 𝑋𝑌 is M (8, 10). One endpoint is Y (1, 2). Find the coordinates of endpoint Y.
Maths-General
Maths-
Solve System of equations using Substitution :
Y = 6X + 7
3X - 8Y = 4
Solve System of equations using Substitution :
Y = 6X + 7
3X - 8Y = 4
Maths-General
Maths-
Two pizzas and four sandwiches cost $62.Four Pizzas and ten sandwiches cost $140.How much does each pizza and sandwich cost ?
Two pizzas and four sandwiches cost $62.Four Pizzas and ten sandwiches cost $140.How much does each pizza and sandwich cost ?
Maths-General
