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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

(−10, 5)

(5,−10)

(10,−5)

(−5, 10)

Answer 1

The intersection point of the two lines given by the equations \(2x + y = 15\) and \(y = -x + 5\) can be found by substituting the second equation into the first.

1. Start with the equation of the second line: \[ y = -x + 5 \]

2. Substitute \(y\) in the first equation: \[ 2x + (-x + 5) = 15 \]

3. Simplify this: \[ 2x - x + 5 = 15 \] \[ x + 5 = 15 \] \[ x = 15 - 5 \] \[ x = 10 \]

4. Now find \(y\) by substituting \(x = 10\) back into the second equation: \[ y = -10 + 5 \] \[ y = -5 \]

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

The correct response is: (10, -5).