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%0D%0A2%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A15%0D%0A and y=−x+5%0D%0A%0D%0A=%0D%0A−%0D%0A%0D%0A+%0D%0A5%0D%0A.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A(−5, 10)%0D%0A(%0D%0A−%0D%0A5%0D%0A,%0D%0A %0D%0A10%0D%0A)%0D%0A left parenthesis negative 5 comma 10 right parenthesis%0D%0A%0D%0A(−10, 5)%0D%0A(%0D%0A−%0D%0A10%0D%0A,%0D%0A %0D%0A5%0D%0A)%0D%0A left parenthesis negative 10 comma 5 right parenthesis%0D%0A%0D%0A(5,−10)%0D%0A(%0D%0A5%0D%0A,%0D%0A−%0D%0A10%0D%0A)%0D%0A left parenthesis 5 comma negative 10 right parenthesis%0D%0A%0D%0A(10,−5)%0D%0A(%0D%0A10%0D%0A,%0D%0A−%0D%0A5%0D%0A)%0D%0Aleft parenthesis 10 comma negative 5 right parenthesis%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AHighlight%0D%0A

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%0D%0A2%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A15%0D%0A and y=−x+5%0D%0A%0D%0A=%0D%0A−%0D%0A%0D%0A+%0D%0A5%0D%0A.%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A￼%0D%0A(−5, 10)%0D%0A(%0D%0A−%0D%0A5%0D%0A,%0D%0A %0D%0A10%0D%0A)%0D%0A  left parenthesis negative 5 comma 10 right parenthesis%0D%0A￼%0D%0A(−10, 5)%0D%0A(%0D%0A−%0D%0A10%0D%0A,%0D%0A %0D%0A5%0D%0A)%0D%0A  left parenthesis negative 10 comma 5 right parenthesis%0D%0A￼%0D%0A(5,−10)%0D%0A(%0D%0A5%0D%0A,%0D%0A−%0D%0A10%0D%0A)%0D%0A  left parenthesis 5 comma negative 10 right parenthesis%0D%0A￼%0D%0A(10,−5)%0D%0A(%0D%0A10%0D%0A,%0D%0A−%0D%0A5%0D%0A)%0D%0Aleft parenthesis 10 comma negative 5 right parenthesis%0D%0ASkip to navigation%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A%0D%0A￼Highlight￼%0D%0A￼￼

Bot GPT 3.5 · Answer

The intersection point of the two linear equations is at (-5, 10).

Step-by-Step Bot · Answer

To find the coordinates of the intersection point, we need to solve the system of equations: Equation 1: 2x + y = 15 Equation 2: y = -x + 5 To solve this system, we can substitute the value of y from Equation 2 into Equation 1: 2x + (-x + 5) = 15 2x - x + 5 = 15 x + 5 = 15 x = 15 - 5 x = 10 Now, substitute the value of x into either of the original equations to find the value of y. Let's use Equation 2: y = -x + 5 y = -10 + 5 y = -5 Therefore, the coordinates of the intersection point are (10, -5).

Explain Bot · Answer

To find the coordinates of the intersection point that solves the system of these two linear equations, we can use the method of substitution. Given the equations: 1) 2x + y = 15 2) y = -x + 5 We can substitute the value of y from equation 2) into equation 1) to find the value of x. Let's do that: Substitute -x + 5 for y in equation 1): 2x + (-x + 5) = 15 Now, simplify the equation by combining like terms: 2x - x + 5 = 15 x + 5 = 15 Next, isolate x by subtracting 5 from both sides: x = 15 - 5 x = 10 Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use equation 2): y = -x + 5 y = -(10) + 5 y = -10 + 5 y = -5 Therefore, the coordinates of the intersection point are (10, -5).