Solve by using substitution. Express your answer as an ordered pair.

Question

{-x+3y=7

{x-4y=-10

Answer 1

1)-x + 3y = 7

2)x - 4y = -10

 

Solve for X in Equation 2: x = 4y - 10.

 

Plug this expression into equation 1: -(4y - 10) + 3y = 7 -> 10 - y = 7 -> y = 3.

 

Solve for x in equation 2: x - 4(3) = -10 -> x = 2.

 

The solutions set is (2,3).

 

We can confirm this by plugging X and Y back into the original equations.

 

1)-2 + 3*3 = 7.

2)2 - 4*(3) = -10.

 

 

Answer 2

Hi Lexi

 

It is exactly the same process as other tutor indicated you before. But, anyway, let me give my answer to you for fixing ideas again.

 

The substitution method consists on represent one unknown variable, for example "x", in terms of a second unknown variable "y", in this case.

 

Because you have a system of equations with two unknown variables "x" and "y", you can use any of these expression to represent x as function of y. I will select the second equation for convenience:  x - 4y = -10

 

Then, I express the unknown variable "x" as function of "y" as follows:  x = 4y - 10  (I just passed the "y" variable to the right).

 

Now, I will substitute this variable "x" in the first equation:  -x + 3y = 7

 

                                                                                      -(4y -10) + 3y = 7

 

Reordering terms, you have:         -4y + 3y +10 = 7

 

Adding terms of the same kind:      -y = -3      It means that y = 3

 

Finally, you can use:   x = 4y - 10

 

                                 x = 4*(3) -10

 

                                 x = 2

 

The pair (x,y) solution of your system of equations is (2,3)