Question

What is the x-coordinate of the point of intersection for the two lines below?
(2x + y = -9
(2x - 5y =-3

Answer 1

Answer:

From the graph, it is clear that the point of intersection is:

• (x, y) = (-4, -1)

And the x-coordinate of the point of intersection for the two lines is:

• x = -4

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

$\begin{bmatrix}2x+y=-9\\ 2x-5y=-3\end{bmatrix}$

solving the system of equations

subtracting 2x+y = -9 from 2x-5y = -3

$2x-5y=-3$

$-$

$\underline{2x+y=-9}$

$-6y=6$

so

$\begin{bmatrix}2x+y=-9\\ -6y=6\end{bmatrix}$

solving for y

$-6y=6$

Divide both sides by -6

$\frac{-6y}{-6}=\frac{6}{-6}$

$y=-1$

$\mathrm{For\:}2x+y=-9\mathrm{\:plug\:in\:}y=-1$

$2x-1=-9$

$2x=-8$

Divide both sides by 2

$\frac{2x}{2}=\frac{-8}{2}$

$x=-4$

Thus, the x-coordinate of the point of intersection for the two lines below will be:

$x=-4$

Also, the graph is attached.

From the graph, it is clear that the point of intersection is:

• (x, y) = (-4, -1)

And the x-coordinate of the point of intersection for the two lines is:

• x = -4