Question

What is the solution to the following system of equations?

y = −x2 − 5x − 4


y = −x2 + 9x − 18

Answer 1

`\left\{\begin{array}{ccc}y=-x^2-5x-4&|change\ signs\\y=-x^2+9x-18\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-y=x^2+5x+4\\y=-x^2+9x-18\end{array}\right}\ \ \ |add\ both\ sides\ of\ the\ equations\\.\ \ \ \ \ \ \ 0=14x-14\ \ \ \ |subtract\ 14x\ from\ both\ sides\\.\ \ -14x=-14\ \ \ \ |divide\ both\ sides\ by\ (-14)\\.\ \ \ \ \ \ x=1\\\\\\subtitute\ the\ value\ of\ x\ to\ the\ equation\ y=-x^2-5x-4\\\\y=-1^2-5\cdot1-4=-1-5-4=-10`

Answer: x = 1 and y = -10