Solving Systems of Equations by Graphing Quick Check%0D%0A2 of 52 of 5 Items%0D%0A%0D%0A%0D%0A%0D%0A%0D%0AQuestion%0D%0AIs (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0? Why?(1 point)%0D%0AResponses%0D%0A%0D%0AYes, because the graphs intersect at (−2, 6).%0D%0AYes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis .%0D%0A%0D%0AYes, because the graphs don’t intersect at (−2, 6).%0D%0AYes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .%0D%0A%0D%0ANo, because the graphs don’t intersect at (−2, 6).%0D%0ANo, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis .%0D%0A%0D%0ANo, because the graphs intersect at (−2, 6).
No, because the graphs don't intersect at (-2, 6).
To determine whether (-2, 6) is a solution to the system of linear equations x + 2y = 10 and 3x + y = 0, we can substitute the values of x and y into the equations and check if they satisfy both equations.
Substituting x = -2 and y = 6 into the first equation:
(-2) + 2(6) = 10
-2 + 12 = 10
10 = 10
The result is true, meaning that (-2, 6) satisfies the first equation.
Substituting x = -2 and y = 6 into the second equation:
3(-2) + (6) = 0
-6 + 6 = 0
0 = 0
The result is also true, meaning that (-2, 6) satisfies the second equation.
Since (-2, 6) satisfies both equations, we can conclude that (-2, 6) is a solution to the system of linear equations.
Therefore, the correct response is:
"Yes, because the graphs intersect at (-2, 6)."
To determine if (−2, 6) is a solution to the system of equations x + 2y = 10 and 3x + y = 0, we need to substitute the values of x and y into both equations and check if the resulting equations are true.
Let's start with the first equation:
x + 2y = 10
Substituting x = -2 and y = 6:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
The equation holds true, so (−2, 6) is a solution to the first equation.
Now let's check the second equation:
3x + y = 0
Substituting x = -2 and y = 6:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Again, the equation holds true, so (−2, 6) is a solution to the second equation as well.
Since (−2, 6) satisfies both the first and the second equations, it is a solution to the system of equations.
The correct response is: "Yes, because the graphs intersect at (−2, 6)."