Question

Solve using the elimination method or the substitution method

5y=4x+10
5x-5y=-10

Answer 1

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

1) \( 5y = 4x + 10 \)
2) \( 5x - 5y = -10 \)

Let’s start by rearranging equation (1) to express \( y \) in terms of \( x \):

\[
5y = 4x + 10
\]

Now, divide both sides by 5:

\[
y = \frac{4}{5}x + 2
\]

Next, we can substitute this expression for \( y \) into equation (2):

\[
5x - 5\left(\frac{4}{5}x + 2\right) = -10
\]

Distributing the \( -5 \):

\[
5x - \left(4x + 10\right) = -10
\]

This simplifies to:

\[
5x - 4x - 10 = -10
\]

Combine like terms:

\[
x - 10 = -10
\]

Adding 10 to both sides gives:

\[
x = 0
\]

Now, substitute \( x = 0 \) back into the equation we derived for \( y \):

\[
y = \frac{4}{5}(0) + 2
\]

This simplifies to:

\[
y = 2
\]

So the solution to the system of equations is:

\[
(x, y) = (0, 2)
\]

### Final Answer:
\((0, 2)\)