What is the solution to the system of equations below? y=3/4x-12 and y=-4x-31

x= -4            and          y = -15 

Step-by-step explanation:

To solve this problem, we will follow the steps below;

y = 3/4 x - 12 ___________________________________(1)

y = -4x - 31 _____________________________________(2)

substitute equation (1) in equation (2)

3/4 x - 12  = -4x - 31

Add 4x to both-side of the equation

3/4 x  + 4x - 12  = -4x + 4x - 31

3/4 x  + 4x - 12  =  - 31

Add 12 to both-side of the equation

3/4 x  + 4x - 12 + 12 =  - 31 + 12

3/4 x  + 4x =  - 31 + 12

 = -19

= -19

Multiply 4 to both-side of the equation

× 4 = -19 × 4

At the left-hand side of the equation, 4 will cancel-out 4, thus the equation becomes;

19x = -19 × 4

Divide both-side of the equation by 19

 =  

(On the left-hand side of the equation 19 at the numerator will cancel out 19 at the denominator leaving us with just x, likewise, on the right-hand side of the equation 19 at the numerator will also cancel-out 19 at the denominator leaving us with -4)

x = -4

Substitute x = -4 into equation (2)

y = -4x - 31

y = -4(-4) - 31

  = 16 - 31

   =-15

y=-15

x= -4            and          y = -15