Solve the system of equation {4x+5y=13 and 3x+y=-4 by the method of substitution

Question

Solve the system of equation {4x+5y=13 and 3x+y=-4 by the method of substitution

Answer 1

Equation (1)---- 4x+5y=13

Equation (2)----3x+ y=-4

 

Isolate y in equation (2) 

3x + y= -4 ------------- subtract 3x from both sides

3x - 3x + y= -4- 3x

y = -4 - 3x

 

Substitute y=-4-3x into equation (1)

 

4x + 5y = 13

4x + 5 (-4-3x) = 13 --------------- Distribute and combine like terms

4x- 20- 15x = 13

-11x - 20 = 13 ----------Add 20 to both sides

-11x = 33 ---------------Divide both sides by -11 to isolate x

-11x/-11 = 33/-11

x = -3

 

Now substitute x = -3 into one of the equations to find y.

 

4x + 5y = 13

4(-3) + 5y = 13

-12 + 5y = 13

5y = 25

y = 5.

 

x=-3

y=5

 

Check the answer by substituting x and y value into original equation/s.