Question

2x+y=1

9x + 3y = -3

The x-coordinate of the point of intersection is

-2
0
5

Answer 1

Answer:

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

Step-by-step 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:

$2x+y=1\\2x=1-y\\x=\frac{1-y}{2}$       Eqn.(1)

Plugging in it, in the second expression we then have

$9(\frac{1-y}{2} )+3y=-3\\\\\frac{9}{2}-\frac{9y}{2}+3y=-3\\ \\\frac{9}{2}-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}\\ \\-\frac{9y}{2}+\frac{6y}{2}=-\frac{6}{2}-\frac{9}{2}\\-3y=-15\\y=\frac{-15}{-3}\\ y=5$

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

$x=\frac{1-5}{2} \\x=\frac{-4}{2}\\ x=-2$

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