Answer:
From the graph, it is clear that the point of intersection is:
And the x-coordinate of the point of intersection for the two lines is:
Step-by-step explanation:
- As we know that the solution of the system of equations is the point of intersection. Let us solve it.
Given the system of equations
[tex]\begin{bmatrix}2x+y=-9\\ 2x-5y=-3\end{bmatrix}[/tex]
solving the system of equations
subtracting 2x+y = -9 from 2x-5y = -3
[tex]2x-5y=-3[/tex]
[tex]-[/tex]
[tex]\underline{2x+y=-9}[/tex]
[tex]-6y=6[/tex]
so
[tex]\begin{bmatrix}2x+y=-9\\ -6y=6\end{bmatrix}[/tex]
solving for y
[tex]-6y=6[/tex]
Divide both sides by -6
[tex]\frac{-6y}{-6}=\frac{6}{-6}[/tex]
[tex]y=-1[/tex]
[tex]\mathrm{For\:}2x+y=-9\mathrm{\:plug\:in\:}y=-1[/tex]
[tex]2x-1=-9[/tex]
[tex]2x=-8[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{-8}{2}[/tex]
[tex]x=-4[/tex]
Thus, the x-coordinate of the point of intersection for the two lines below will be:
[tex]x=-4[/tex]
Also, the graph is attached.
From the graph, it is clear that the point of intersection is:
And the x-coordinate of the point of intersection for the two lines is:
