Hi! -2x + y = -11 4x + 4y = 4 System by substitution!!!

Point Form:

(

8

3

,

−

5

3

)

Equation Form:

x

=

8

3

,

y

=

−

5

3

x=4, y=-3, or (4,-3)

Step-by-step explanation:

Hi there!

We are given the following system of equations:
-2x+y=-11

4x+4y=4

And the problem wants us to solve it by substitution

In substitution, we will solve one of the equations for one of the variables to equal an expression containing the other variable, then substitute that expression as the variable it equals into the other equation, solve that equation, then use the value of the solved variable to solve for the first equation we made (the one that is a variable equaling an expression containing the other variable)

It's easier to do this when one of the variables already has a coefficient of 1, as we can just move a couple of terms around without having to multiply or divide anything; for example, in the first equation, -2x+y=-11, y already has a coefficient of 1

So we can just add 2x to both sides, in order to solve the equation for y

-2x+y=-11

+2x      +2x

y=2x-11

Now substitute this expression into the the second equation as y.

So, 4x+4y=4 would become 4x+4(2x-11)=4

Now we need to solve 4x+4(2x-11)=4

Do the distributive property:

4x+8x-44=4

Combine like terms

12x-44=4

Add 44 to both sides

12x=48

x=4

We found the value of x

Now we need to find the value of y
Substitute 4 as x in y=2x-11

y=2(4)-11

Multiply

y=8-11

subtract

y=-3

The answer is x=4, y=-3, or as a point, (4, -3)
Hope this helps!
See more on solving systems by substitution here:

table 3 represents a direct variation function. : )