Question

What is the x-coordinate of the point of intersection for the two lines below?

(2x + y = -9
(2x - 5y =-3

Answer 1

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

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

`(-6y)/(-6)=(6)/(-6)`

`y=-1`

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

`2x-1=-9`

`2x=-8`

Divide both sides by 2

`(2x)/(2)=(-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