Question

find the coordinates of the intersection point that solves the system of these two linear eqations in two variabals: 2x + y = 15 and y = -x + 5

A. (-5, 10
B. (10, -5)
C. (5,-10)
D. (-10, 5)

Answer 1

To solve the system of equations, we can use the method of substitution.

First, we solve the second equation for y:
y = -x + 5

Next, we substitute this expression for y in the first equation:
2x + (-x + 5) = 15

Simplifying the equation:
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10

Now that we have the value of x, we can substitute it back into either of the original equations to find the value of y. Let's substitute it into the second equation:

y = -x + 5
y = -10 + 5
y = -5

Therefore, the intersection point is (10, -5), which corresponds to option B.