Solve a system of quadratic equations, algebra homework help

I have listed the questions and explanation below. Please help me understand them better and help me solve these types of problems. Thank you.

Solve the system of equations.
y-33x + 47
y = *- 33x – 2
Write the coordinates in exact form. Simplify all fractions and radicals.
You answered:
If a system of equations includes a linear equation and a quadratic equation (parabola,
circle, ellipse, or hyperbola), then solve using substitution.
Look at the system of equations:
y = -33x + 47
Line
y = x2 – 33x – 2
Parabola
Since there is a linear equation, it’s best to use substitution.
Notice that the parabolic equation has an x term, but no y term. To avoid squaring, it’s best
to isolate y in the linear equation. Luckily, it’s already isolated: y = -33x + 47.
Substitute y = -33x + 47 into the parabolic equation and solve for x.
2
Y-X – 33x-2
-33x + 47 – x
2
– 33x – 2
49×2
+7= x
Finally, plug x = 7 and x = -7 into one of the original equations to find the solutions. It’s easier
to use the linear equation.
Plug in x = 7.
y = -33x + 47
= -33(7) + 47
=-231 +47
= -184
The solution is (7. – 184).
Plug in x = -7.
y=-33x + 47
= -33(-7) + 47
= 231 + 47
= 278
The solution is (-7, 278).
So, the line y = -33x + 47 and the parabola y = x2 – 33x – 2 intersect at two points:
(7.-184) and (-7, 278)