Question

Solve the system: y = 2x 3 y = -x 6 what is the point of intersection? ( x , y )

a) (2, 3)
b) (1, 5)
c) (2, 5)
d) (1, 3)

Answer 1

By setting the given equations equal to each other and solving for x, we find the x-coordinate of the intersection to be 1. Substituting this value back into one of the original equations gives us a y-coordinate of 5. Therefore, the point of intersection is (1, 5), option b).

Step-by-step explanation:

To solve the system of equations and find the point of intersection, we can set the two equations equal to each other since they both equal y:

• y = 2x + 3
• y = -x + 6

Now, let's set them equal to each other to find the x-coordinate of the intersection:

2x + 3 = -x + 6

Add x to both sides:

3x + 3 = 6

Subtract 3 from both sides:

3x = 3

Divide by 3:

x = 1

Substitute x = 1 into either original equation to find y:

y = 2(1) + 3

y = 5

Thus, the point of intersection is (1, 5), which corresponds to option b).