Question

solve the system of equations: y=5x y=x^2+5x-9

Answer 1

To solve the system of equations given by:

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

we can set them equal to each other since both expressions represent \( y \):

\[
5x = x^2 + 5x - 9
\]

Next, we can simplify this equation by subtracting \( 5x \) from both sides:

\[
0 = x^2 + 5x - 9 - 5x
\]

This simplifies to:

\[
0 = x^2 - 9
\]

Now, we can factor the quadratic:

\[
0 = (x - 3)(x + 3)
\]

Setting each factor equal to zero gives us the possible values for \( x \):

1. \( x - 3 = 0 \) → \( x = 3 \)
2. \( x + 3 = 0 \) → \( x = -3 \)

Now, we can find the corresponding \( y \) values for each \( x \).

For \( x = 3 \):

\[
y = 5(3) = 15
\]

For \( x = -3 \):

\[
y = 5(-3) = -15
\]

Thus, the solution set for the system of equations is:

\[
(3, 15) \quad \text{and} \quad (-3, -15)
\]

So, the solutions are:

1. \( (3, 15) \)
2. \( (-3, -15) \)