Question

Solve the system by substitution.
minus, 3, y, equals, x
−3y=
x
minus, 8, x, plus, 2, y, equals, 26
−8x+2y=
26

Answer 1

To solve the system of equations by substitution, we first rewrite the equations clearly:

1. \( -3y = x \) (which we can also write as \( x = -3y \))
2. \( -8x + 2y = 26 \)

Next, we'll use the expression for \( x \) from the first equation to substitute into the second equation.

Substituting \( x = -3y \) into the second equation:

\[
-8(-3y) + 2y = 26
\]

Now, simplify the equation:

\[
24y + 2y = 26
\]

Combine like terms:

\[
26y = 26
\]

Now, solve for \( y \):

\[
y = 1
\]

Now that we have the value of \( y \), we can substitute it back into the first equation to find \( x \):

\[
x = -3y = -3(1) = -3
\]

Thus, the solution to the system of equations is:

\[
x = -3, \quad y = 1
\]

In ordered pair form, the solution is:

\[
(-3, 1)
\]

This means \( x = -3 \) and \( y = 1 \).