Solve the simultaneous equations...

Question

Solve the simultaneous equations y=5x²+4x-19 and y=4x+1.

I thought the answer would only be x=something and y=something but apparently there is x=something, y=something and then another row of x=something and y=something?? The answers they gave was x=2 and -2 and y=9 and -7 if that helps anyone help me. I’m preparing for exams and any assistance will be GREATLY appreciated :).

Answer 1

set them equal

5x^2 +4x -19 = 4x +1

5x^2 = 20

x^2 = 20/5 = 4

x= + or - sqr4

x = + or - 2

for x=+2, y = 4(2)+1 = 9 that's the point (2,9)

for x=-2, y = 4(-2)+1 = -7, that's the point (-2,-7)

If you graph the 2 equations, you get a straight line that intersects a parabola at those two points

It's a U shaped, upward opening parabola with vertex at (-2/5, - 19 4/5)

the linear equation is a line with slope 4 and y intercept 1. It intersects the parabola in quadrants I and III

It's like a line cutting a huge letter U in two places, on the left side of the U and also on the right side