Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AFind 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.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(5,−10)%0D%0A left parenthesis 5 comma negative 10 right parenthesis%0D%0A%0D%0A(10,−5)%0D%0Aleft parenthesis 10 comma negative 5 right parenthesis%0D%0A%0D%0A(−5, 10)%0D%0A left parenthesis negative 5 comma 10 right parenthesis%0D%0A%0D%0A(−10, 5)

Question

Use the image to answer the question.%0D%0A%0D%0A%0D%0A%0D%0AFind 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.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(5,−10)%0D%0A  left parenthesis 5 comma negative 10 right parenthesis%0D%0A%0D%0A(10,−5)%0D%0Aleft parenthesis 10 comma negative 5 right parenthesis%0D%0A%0D%0A(−5, 10)%0D%0A  left parenthesis negative 5 comma 10 right parenthesis%0D%0A%0D%0A(−10, 5)

GPT 3.5 · Answer

To find the coordinates of the intersection point, we can solve the system of equations:

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

We can solve this system by substituting the second equation into the first equation:

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

Now we can substitute this value of x back into either of the equations to solve for y. Let's use the second equation:

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

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