What is the x,y-coordinate for the solution of the system of equations below

Question

2y+x=12 
4y-x=-18

Answer 1

Substitution Method :

The system of equations are 2y + x = 12 and 4y - x = - 18.

Step 1 : Solve the equation 1: 2y + x = 12 for x since the coefficient is 1.

Subtract 2y from each side.

2y + x - 2y = 12 - 2y

x = 12 - 2y

 

Step 2 : Substitute (12 - 2y) for x in the equation 2 : 4y - x = - 18 to find the value of y.

4y - (12 - 2y) = - 18

Apply distributive property : a(b - c) = ab - ac.

4y - 12 + 2y = - 18

6y - 12 = - 18

Add 12 to each side.

6y - 12 + 12 = - 18 + 12

6y = - 6

Divide each side by 6.

6y/6 = - 6/6

y = - 1.

 

Step 3 : Substitute - 1 for y in either equation to find x.

Equation 1: 2y + x = 12.

2(-1) + x = 12

- 2 + x = 12

Add 2 to each side.

- 2 + x + 2 = 12 + 2

x = 14.

 

The solution is (14, -1).