Solve 7x+2y=8, - 5x-2y=-12 by elimination/addition

Answer: (-2, 11) That is, x = - 2 and y = 11

Step-by-step explanation: We have a pair of simultaneous equations and since none of the variables has a coefficient of 1, we shall solve by use of the elimination method. The equations are

7x + 2y = 8 - - - (1)

-5x - 2y = - 12 - - (2)

The coefficients of the y variable in both equations is 2 in either case. So straight away, we add both equations together. (This is because of the negative sign in one the coefficients of y).

Adding both equations results in;

(7x + - 5x) + (2y + - 2y) = (8 + - 12)

2x = - 4

Divide both sides of the equation by 2

x = - 2

Having calculated x, we now substitute for the value of x into equation (1)

7x + 2y = 8

7 (-2) + 2y = 8

-14 + 2y = 8

Add 14 to both sides of the equation

2y = 22

Divide both sides of the equation by 2

y = 11

Therefore, x = - 2 and y = 11