Question

would (3, 11) and (−3, −7) be the answer to What are the solutions to the following system of equations?
y = x2 + 3x − 7
3x − y = −2

Answer 1

Here's how you find out:

plug \((x=3,y=11)\) into both equations. Do they both work with those values? If so, it is a solution.

Answer 2

i think so

Answer 3

Here's what I mean:

\[y = x^2+3x-7\]Plug in \(x-3,y=11\)
\[11=(3)^2+3(3) - 7\]\[11=9+9-7\]\[11=11\checkmark\]\[3x-y=-2\]\[3(3)-11=-2\]\[9-11=-2\]\[-2=-2\checkmark\]

That shows the point \((3,11)\) is a solution to the system.

Answer 4

The other one is correct as well. Good job!

Answer 5

Here's a graph showing the line and the parabola and their intersection at the solutions.