Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x+y=15 and y=−x+5

Question

(5,−10)

(−10, 5)

(−5, 10)

(10,−5)

Answer 1

To find the intersection point, we can substitute the second equation into the first equation:

2x + y = 15
2x + (-x + 5) = 15
2x - x + 5 = 15
x + 5 = 15
x = 10

Now that we have found x=10, we can plug it back into the second equation to find y:

y = -10 + 5
y = -5

Therefore, the coordinates of the intersection point are (10, -5), which is the fourth option.