Respuesta :
To find what we are looking for we first need to find the second equation.
To do this we need to use the equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]where (x1,y1) is a point on the line and m is the slope. The slope of a line is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Using the first two points on the table we get:
[tex]\begin{gathered} m=\frac{-4-8}{3-(-1)} \\ =\frac{-12}{4} \\ =-3 \end{gathered}[/tex]Now that we have the slope we plug it in the equation of a line with the values of any of the points in the table (we are going to use the first one). Then:
[tex]\begin{gathered} y-8=-3(x-(-1)) \\ y-8=-3(x+1) \\ y-8=-3x-3 \\ 3x+y=5 \end{gathered}[/tex]Now that we have the equation of the second line we conclude that we have the system of equations:
[tex]\begin{gathered} 2x+4y=0 \\ 3x+y=5 \end{gathered}[/tex]To find the x value of the solution we solve the second equation for y, then:
[tex]y=5-3x[/tex]now we plug this value into the first equation and solve for x:
[tex]\begin{gathered} 2x+4(5-3x)=0 \\ 2x+20-12x=0 \\ -10x=-20 \\ x=\frac{-20}{-10} \\ x=2 \end{gathered}[/tex]Therefore, the x value of the solution of the system is 2.
