is (-2, 6) a solution to the system of these linear equations: x + 2y = 10 and 3x + y = 0
A. no, because the graphs intersect at (-2, 6)
B. no because the graphs dont intersect at (-2, 6)
C. yes, because the graphs intersect at (-2, 6)
D. yes because the graphs dont intersect at (-2, 6)
To determine if (-2, 6) is a solution to the system of linear equations, we substitute the values of x and y into the equations and check if they are satisfied.
For the first equation, x + 2y = 10:
(-2) + 2(6) = 10
-2 + 12 = 10
10 = 10
For the second equation, 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Both equations are satisfied when x = -2 and y = 6. Therefore, (-2, 6) is a solution to the system of linear equations.
The correct answer is: C. yes, because the graphs intersect at (-2, 6)
To determine if (-2, 6) is a solution to the system of linear equations, we can substitute the values of x and y into both equations and see if they are satisfied.
1. Substituting x = -2 and y = 6 into the first equation, we have:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
2. Substituting x = -2 and y = 6 into the second equation, we have:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Since both equations are satisfied when we substitute (-2, 6) for x and y, we can conclude that (-2, 6) is a solution to the system of linear equations.
Therefore, the answer is:
C. Yes, because the graphs intersect at (-2, 6).
To determine if (-2, 6) is a solution to the system of linear equations, we substitute the values of x and y into the two equations and check if both equations are satisfied.
Let's substitute the values x = -2 and y = 6 into the first equation: x + 2y = 10.
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
Since the left-hand side of the equation is equal to the right-hand side, the first equation is satisfied.
Now, let's substitute the values x = -2 and y = 6 into the second equation: 3x + y = 0.
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Again, the left-hand side of the equation is equal to the right-hand side, so the second equation is satisfied.
Since (-2, 6) satisfies both equations, it is a solution to the system.
Therefore, the answer is C. Yes, because the graphs intersect at (-2, 6).