Question

Solve the system of equations using substitution.
5x-2y=-6
y=3x+3



(0,3)


(0, -3)


(-3,0)


(3,0)

Answer 1

To solve the system of equations using substitution, we have the equations:

1. \( 5x - 2y = -6 \)
2. \( y = 3x + 3 \)

We can substitute the expression for \(y\) from the second equation into the first equation.

Substituting \(y = 3x + 3\) into the first equation:

\[
5x - 2(3x + 3) = -6
\]

Now, simplify this equation:

\[
5x - 6x - 6 = -6
\]

Combine like terms:

\[
-1x - 6 = -6
\]

Adding 6 to both sides gives:

\[
-1x = 0
\]

Thus:

\[
x = 0
\]

Now that we have \(x\), we can find \(y\) by substituting \(x = 0\) back into the second equation:

\[
y = 3(0) + 3 = 3
\]

So we have the solution:

\[
(x, y) = (0, 3)
\]

The answer is \((0, 3)\).