Question

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.

Answer 1

To find the intersection point, we need to solve the system of equations:

1) 2x + y = 15
2) y = -x + 5

We can substitute equation 2 into equation 1:
2x + (-x + 5) = 15
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10

Substitute this value of x into equation 2 to find y:
y = -10 + 5
y = -5

Therefore, the intersection point is (10, -5).