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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