Answer:
[tex]x_{1}=-4[/tex]
[tex]x_{2}=-6[/tex]
[tex]y=-4[/tex]
Step-by-step explanation:
We have the following equations:
[tex]y=-3x^{2}-30x-76[/tex] (1)
[tex]y=2x^2+20x+44[/tex] (2)
Multiplying (1) by [tex]2[/tex] and (2) by [tex]3[/tex]:
[tex]2y=-6x^{2}-60x-152[/tex] (3)
[tex]3y=6x^2+60x+132[/tex] (4)
Summing (3) and (4):
[tex]5y=-20[/tex] (5)
Isolating [tex]y[/tex]:
[tex]y=-4[/tex] (6)
Substituting (6) in (2):
[tex]-4=2x^2+20x+44[/tex] (7)
Rearranging the equation:
[tex]0=x^2+10x+24[/tex] (8)
Solving with the quadratic formula [tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex], where [tex]a=1[/tex], [tex]b=10[/tex], [tex]c=24[/tex], in order to find the two values of [tex]x[/tex] that satisfy the system of equations:
[tex]x=\frac{-10\pm\sqrt{10^{2}-4(1)(24)}}{2(1)}[/tex] (9)
[tex]x_{1}=-4[/tex] (10)
[tex]x_{2}=-6[/tex] (11)
