Use the image to answer the question.
A coordinate plane with four quadrants shows the x-axis ranging from negative 5 to 15 in increments of 1 and the y-axis ranging from negative 10 to 10 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is 2 x plus y equals 15. The equation of the dotted line is y equals negative x plus 5. The intersection of both lines is shown at positive 10 on the x-axis and negative 5 on the y-axis in quadrant 4.
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
(5,−10)
left parenthesis 5 comma negative 10 right parenthesis
(−5, 10)
left parenthesis negative 5 comma 10 right parenthesis
(−10, 5)
left parenthesis negative 10 comma 5 right parenthesis
(10,−5)
left parenthesis 10 comma negative 5 right parenthesis
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The correct answer is (10, -5).
From the given information, we know that the equations of the solid line and the dotted line are:
1) 2x + y = 15
2) y = -x + 5
To find the coordinates of the intersection point, we need to solve this system of equations. We can do this by substituting the second equation into the first equation and solving for x.
Substituting y = -x + 5 into 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 one of the original equations to find the value of y. Let's use the second equation:
y = -x + 5
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point are (10, -5).
To find the coordinates of the intersection point, we need to solve the system of equations:
1. 2x + y = 15
2. y = -x + 5
We can solve this system by substitution or elimination. Let's use substitution:
Step 1: Substitute equation 2 into equation 1.
2x + (-x + 5) = 15
Step 2: Simplify the equation.
2x - x + 5 = 15
x + 5 = 15
Step 3: Solve for x.
x = 15 - 5
x = 10
Step 4: Substitute the value of x into equation 2 to find y.
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point are (10, -5).