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y=-x+ 5 x 10- -9- -8- -7- -6- -4- -3- -2- 1. -0- -5 -4 -3 -2 -1,0 -1- O (-5, 10) O (5,-10) O (10,-5) O (-10, 5) -2- -3- -4- -5- -6+ -7+ -8- -9- -10 2x + y = 15 1 2 3 4 jo 7 8 9 10 11 12 13 14 15 x 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. (1 point)

1 answer

To find the intersection point of the two linear equations, we can solve the system of equations by substitution or elimination. Let's use substitution.

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

Next, we'll substitute this value of y into the first equation, 2x + y = 15:
2x + (-x + 5) = 15

Simplifying the equation, we get:
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 the second equation to find y:
y = -x + 5
y = -10 + 5
y = -5

Therefore, the coordinates of the intersection point are (10, -5).