Question

find all solutions of the system of equations algebraically. write your solutions as coordinate points.
y = x² + x - 18
14 = x - y
answer
two solutions
and
submit answer

Explanation:

Step1: Solve the second equation for y

From \(14 = x - y\), we can rearrange it to get \(y = x - 14\).

Step2: Substitute y into the first equation

Substitute \(y = x - 14\) into \(y = x^{2}+x - 18\). So we have \(x - 14=x^{2}+x - 18\).

Step3: Simplify the equation

Subtract \(x\) from both sides: \(- 14=x^{2}-18\). Then add 18 to both sides: \(x^{2}=4\).

Step4: Solve for x

Take the square root of both sides, we get \(x=\pm2\).

Step5: Find the corresponding y values

• When \(x = 2\), substitute into \(y=x - 14\), then \(y=2 - 14=-12\).
• When \(x=- 2\), substitute into \(y=x - 14\), then \(y=-2 - 14=-16\).

Answer:

\((2, - 12)\) and \((-2, - 16)\)