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.

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)
  left parenthesis negative 10 comma 5 right parenthesis

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

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

(5,−10)

GPT-4o mini · Answer

To find the coordinates of the intersection point that solves the system of equations:

Equation of the solid line: \(2x + y = 15\)
Equation of the dotted line: \(y = -x + 5\)

We can substitute the expression for \(y\) from the second equation into the first equation.

Substituting \(y = -x + 5\) into \(2x + y = 15\):

\[ 2x + (-x + 5) = 15 \]

Simplifying this equation:

\[ 2x - x + 5 = 15 \ x + 5 = 15 \ x = 10 \]

Now, substitute \(x = 10\) back into the equation \(y = -x + 5\) to find \(y\):

\[ y = -10 + 5 = -5 \]

Thus, the intersection point of the two lines is \((10, -5)\).

So the answer is:

\[ \text{(10, −5)} \]