Respuesta :
ANSWER
[tex]\begin{gathered} x=-4,y=8 \\ x=5,y=35 \end{gathered}[/tex]EXPLANATION
We want to find the values of x and y from the given system of equations:
[tex]\begin{gathered} y=x^2+2x \\ y=3x+20 \end{gathered}[/tex]To do this, subsitute the second equation into the first:
[tex]\begin{gathered} 3x+20=x^2+2x \\ \text{Collect like terms:} \\ x^2+2x-3x-20=0 \\ x^2-x-20=0 \end{gathered}[/tex]Now, solve by factorization:
[tex]\begin{gathered} x^2-5x+4x-20=0 \\ x(x-5)+4(x-5)=0 \\ (x+4)(x-5)=0 \\ x+4=0;x-5=0_{} \\ \Rightarrow x=-4;x=5 \end{gathered}[/tex]Now, substitute the values of x into the second equation to find the values of y:
[tex]\begin{gathered} \text{when x = -4} \\ y=3(-4)+20 \\ y=-12+20 \\ y=8 \\ \text{when x = 5:} \\ y=3(5)+20 \\ y=15+20 \\ y=35 \end{gathered}[/tex]Therefore, the values of x and y are:
[tex]\begin{gathered} x=-4,y=8 \\ x=5,y=35 \end{gathered}[/tex]