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.

(1 point)
Responses

(−10, 5)
left parenthesis negative 10 comma 5 right parenthesis

(−5, 10)
left parenthesis negative 5 comma 10 right parenthesis

(5,−10)
left parenthesis 5 comma negative 10 right parenthesis

(10,−5)
left parenthesis 10 comma negative 5 right parenthesis

Answer 1

To find the intersection point, we can substitute the value of 'y' from the second equation into the first equation.

y = -x + 5

Substituting this value into the first equation:
2x + (-x + 5) = 15

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

Now, substitute this value of 'x' into the second equation to find 'y':
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5

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