Question

What are the solutions to the following system of equations? y = x2 + 3x − 7 3x − y = −2

Answer 1

x = -3, y = -7

x = 3, y = 11

Explanation:

Given that two equations;

y = x² + 3x − 7 ---------------- (1)

3x − y = −2 -----------------------(2)

Solve equation (2) for y

y = 3x + 2

Now plug the value of y into the equation (1)

y = x² + 3x − 7

3x + 2 = x² + 3x - 7

Write it in standard quadratic form.

x² + 3x - 3x - 7 - 2 = 0

x² - 9 = 0

x² = 9

take square root both the side

x = ± 3

Now find the value of y

put x = 3 into the equation (2)

3x - y = -2

3(3) - y = -2

y = 11

So, at x = 3, y=11

Now x = -3

3(-3) - y = -2

y = -7

At x = -3 , y = -7

That's the final answer.