Question

Solve using the elimination method.

x+3y=0
5x+2y=-26

Answer 1

To solve the system of equations using the elimination method, we have the following equations:

1. \( x + 3y = 0 \) (Equation 1)
2. \( 5x + 2y = -26 \) (Equation 2)

First, we'll manipulate Equation 1 to express \(x\) in terms of \(y\):

From Equation 1:
\[ x = -3y \]

Now, we can substitute \(x\) in Equation 2 with \(-3y\):

Substituting into Equation 2:
\[ 5(-3y) + 2y = -26 \]

Now simplify:
\[ -15y + 2y = -26 \]
\[ -13y = -26 \]

Next, solve for \(y\):
\[ y = \frac{-26}{-13} \]
\[ y = 2 \]

Now that we have \(y\), we can substitute it back into the expression for \(x\):
\[ x = -3y \]
\[ x = -3(2) \]
\[ x = -6 \]

Thus, the solution to the system of equations is:
\[ x = -6, \quad y = 2 \]

So the final answer is:
\[
(x, y) = (-6, 2)
\]