Question

-10x+3y=34
Y=-8x
Solve by substitution

Answer 1

To solve the system of equations using substitution, we start with the two equations given:

1. \( -10x + 3y = 34 \)
2. \( y = -8x \)

Since the second equation is already solved for \( y \), we can substitute this expression into the first equation.

Substituting \( y = -8x \) into \( -10x + 3y = 34 \):

\[
-10x + 3(-8x) = 34
\]

Now, simplify the equation:

\[
-10x - 24x = 34
\]

Combine the terms:

\[
-34x = 34
\]

Next, solve for \( x \):

\[
x = \frac{34}{-34} = -1
\]

Now that we have \( x \), we can find \( y \) using the expression for \( y \) in the second equation:

\[
y = -8x
\]

Substitute \( x = -1 \):

\[
y = -8(-1) = 8
\]

Therefore, the solution to the system of equations is:

\[
(x, y) = (-1, 8)
\]

To summarize, the final answer is:

\[
\boxed{(-1, 8)}
\]