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# What are the solutions to the following system of equations? y = x^{2} + 3x − 7 3x − y = −2 # What are the solutions to the following system of equations? y = x^{2} + 3x − 7 3x − y = −2

Question
Systems of equations asked 2020-10-25
What are the solutions to the following system of equations?
$$y = x^{2} + 3x − 7$$
$$3x − y = −2$$

## Answers (1) 2020-10-26

$$y = x^{2} + 3x - 7$$
$$3x - y = -2$$
I'll plug the top into the bottom since it is already y=
$$3x - (x^{2} + 3x - 7) = -2$$
distribute the negative and get rid of parenthesis
$$3x - x^{2} - 3x + 7 = -2$$
condense $$-x^{2} + 7 = -2$$
re-write as quadratic with positive $$x^{2}$$
$$x^{2} - 9 = 0$$
solve for x
$$x = -3$$,
$$x = 3$$
plug in each x to get its y
$$y = -7$$,
$$y = 11$$
solutions: (-3,-7) and (3,11)

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