Question

Solve the linear system using substitution
y-2x=-6
5x-y=9

Answer 1

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

1. \( y - 2x = -6 \)
2. \( 5x - y = 9 \)

First, we can solve one of the equations for one variable. Let's solve equation (1) for \( y \):

\[
y = 2x - 6
\]

Now, we can substitute this expression for \( y \) into the second equation (equation 2):

\[
5x - (2x - 6) = 9
\]

Now, simplify the equation:

\[
5x - 2x + 6 = 9
\]
\[
3x + 6 = 9
\]

Next, subtract 6 from both sides:

\[
3x = 3
\]

Now, divide by 3:

\[
x = 1
\]

Now that we have the value of \( x \), we can substitute it back into the expression we found for \( y \):

\[
y = 2(1) - 6
\]
\[
y = 2 - 6
\]
\[
y = -4
\]

So the solution to the system of equations is:

\[
x = 1, \quad y = -4
\]

Finally, we can write the solution as an ordered pair:

\[
(1, -4)
\]

This is the solution to the system of equations.