Question

Solve the following system.

y = -2x^2 + 3x - 1 and x + y = -1.

The solutions are
and

Answer 1

How would you like to solve the system of equations?

We can use the substitution method and solve a quadratics equation or we could graph the two equations and find their points of intersection.

Do you know how to substitute the first equation into the second one?
Or how to graph the equations to find where they intersect?

Answer 2

For the substitution method, let me add some colors

\( \color{red}{y} = \color{red}{-2x^2 + 3x - 1}\)

and

\( x + \color{red}{y} = -1\)

since y = that long equation

you can replace the y in the second equation with that long thing

like

\( x +( \color{red}{-2x^2 + 3x - 1}) = -1\)

so now we have
\( x -2x^2 + 3x - 1= -1\)

can you simplify it and solve for x?

Answer 3

If you want to graph it, you can use: https://www.desmos.com/calculator