Solve by system of substitution.
y = 2x - 6
6x - 2y = 22

Question

Solve by system of substitution. 
y = 2x - 6
6x - 2y = 22

thekidwithnoanswers · Answer

i know i need to find x and y but i dont know how to find them

mathstudent55 · Answer

You are asked to use the substitution method.
The substitution method is used to solve systems of equations.
Let's say you have a system of 2 equations, like you do.
The first step is to solve one equation for one unknown.
If you look at your two equations, you will notice that the first equation is already solved for y, so the first step in the substitution method is already done.
The next step is to take what y is equal to and substitute it in the other equation where you see y.

Here is the second equation:

$\large 6x - 2\color{red}{y} = 22$

Where you see y (in red above) in the second equation, substitute what y is equal to from the first equation (in red below).

$\large y = 2x - 6$

Substitute 5 for x:

$\large y = 2(5) - 6$

$\large = 10 - 6$

$\large y = 4$


$\large y = \color{red}{2x - 6}$

After the substitution, the second equation becomes:

$\large 6x - 2\color{red}{(2x - 6)} = 22$

What the substitution accomplished is that you now have one equation in only one unknown, x, so you can solve for x.

$\large 6x - 2(2x - 6) = 22$

$\large 6x - 4x + 12 = 22$

$\large 2x + 12 = 22$

$\large 2x = 10$

$\large x = 5$

We now have that x = 5. We need to find y.
Now you use substitution again to find y.
Take either one of the original equations, and substitute x with the value of x we just found. Then solve for y. Let's use the first equation:

mathstudent55 · Answer

$\large y = 2x - 6$

$\large y = 2(5) - 6$

$\large y = 10 - 6$

$\large y = 4$

The solution is: x = 5 and y = 4.

Now we can check to see if the solution is correct.
Substitute x = 5 and y = 4 in each solution to see if it makes both equations true.

y = 2x - 6 
4 = 2(5) - 6
4 = 10 - 6
4 = 4
Our solution works on the first equation.

6x - 2y = 22
6(5) - 2(4) = 22
30 - 8 = 22
22 = 22
Our solution also works in the second equation.

Our solution is correct.

thekidwithnoanswers · Answer

dear god thank you so much.

mathstudent55 · Answer

You're welcome.