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

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

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)

### Relevant Questions

Solve each system of equation. Then, check the solutions by substituting them into the original equations to see if the equations are true.
$$x+2y=8. x=-5$$

Find the augmented matrix for the following system of linear equations:
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What is the solution of the system of equations?
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A (2, 1)
B (1, 2)
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D (1, -1)
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x-3y=2
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Consider the following system of linear equations:
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Solve the system of equations (Use matrices.):
$$x-2y+z = 16$$,
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$$\left\{\begin{matrix} 3x−y=1 \\ 2x+3y=8 \end{matrix}\right\}$$
$$\log_{7}(x+2)=\log_{7}(14)−\log_{7}(x−3)$$