Question

The following system of equations intersects at one point. What is the y-coordinate of this point?

n(x) = -x + 2
p(x) = 3x + 6
a) -1
b) 2
c) 6
d) 3

Answer 1

To find the y-coordinate of the point where the two equations intersect, solve the system of equations by setting them equal to each other and solving for x. Substitute the x-coordinate into one of the equations to find the y-coordinate.

Step-by-step explanation:

To find the y-coordinate of the point where the two equations intersect, we need to solve the system of equations. The given equations are n(x) = -x + 2 and p(x) = 3x + 6. To solve the system, we will set the two equations equal to each other and solve for x.

-x + 2 = 3x + 6

First, we will simplify the equation by combining like terms. Add x to both sides to isolate the x term on one side:

2 = 4x + 6

Next, subtract 6 from both sides to isolate the x term: -4 = 4x

Divide both sides by 4 to solve for x: x = -1

Now that we have the x-coordinate, we can substitute it back into either of the original equations to find the y-coordinate. Let's use the equation n(x) = -x + 2:

n(-1) = -(-1) + 2

n(-1) = 1 + 2

n(-1) = 3

Therefore, the y-coordinate of the point where the two equations intersect is 3.