Question

The first equation tells you that y equals 3x−2. So, one way to start solving this system of equations is to substitute 3x−2 anywhere you see y in the second equation. Go for it. Substitute 3x−2 for y in the second equation.
y= 3x−2
x= −2y+10
x = −2(
) + 10

Answer 1

Sure! We can substitute \( y = 3x - 2 \) into the second equation \( x = -2y + 10 \).

Here’s how it looks:

Starting with the second equation:

\[
x = -2y + 10
\]

Substituting \( y = 3x - 2 \) into this equation gives:

\[
x = -2(3x - 2) + 10
\]

Now, let's simplify that:

\[
x = -6x + 4 + 10
\]

Combine like terms:

\[
x = -6x + 14
\]

Now, add \( 6x \) to both sides:

\[
x + 6x = 14
\]

This simplifies to:

\[
7x = 14
\]

Now, divide both sides by 7:

\[
x = 2
\]

Now that we have \( x \), we can substitute back to find \( y \):

Using the first equation \( y = 3x - 2 \):

\[
y = 3(2) - 2 = 6 - 2 = 4
\]

So the solution to the system of equations is:

\[
x = 2, \quad y = 4
\]