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)
The coordinates of the intersection point are (10,-5).
Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?
To determine if (-2,6) is a solution to the system of linear equations x+2y=10 and 3x+y=0, we substitute x=-2 and y=6 into each equation to see if both equations are true with these values.
For the first equation, x + 2y = 10:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10 (True)
For the second equation, 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0 (True)
Since both equations are true when x=-2 and y=6, the point (-2,6) is a solution to the system of linear equations.
Answer Choices
No, because the graphs intersect at (−2, 6).No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .No, because the graphs don’t intersect at (−2, 6).No, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .Yes, because the graphs intersect at (−2, 6).Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .Yes, because the graphs don’t intersect at (−2, 6).Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .