Question

2x+y=1

9x + 3y = -3

The x-coordinate of the point of intersection is

-2
0
5

Answer 1

The x-coordinate of the point of intersection is -2

Explanation:

Here we have a typical system of linear equations whose solution will give us both the x- and the y- coordinates (i.e. the intersection point).

Let us solve the system and find which matches the available options, as follow. Given:

`2x+y=1\\9x+3y=-3`

Taking the first expression and re arranging to solve for
`x` we have:

`2x+y=1\\2x=1-y\\x=(1-y)/(2)` Eqn.(1)

Plugging in it, in the second expression we then have

`9((1-y)/(2) )+3y=-3\\\\(9)/(2)-(9y)/(2)+3y=-3\\ \\(9)/(2)-(9y)/(2)+(6y)/(2)=-(6)/(2)\\ \\-(9y)/(2)+(6y)/(2)=-(6)/(2)-(9)/(2)\\-3y=-15\\y=(-15)/(-3)\\ y=5`

So finally plugging in the y value in Eqn.(1) we have

`x=(1-5)/(2) \\x=(-4)/(2)\\ x=-2`

The x-coordinate of the point of intersection is -2