Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0? Why?(1 point) give an in depth answer
To determine if (-2, 6) is a solution to the system of linear equations, we can plug in the values of x and y into each equation and see if they hold true.
First, let's plug in (-2, 6) into the first equation x + 2y = 10:
(-2) + 2(6) = 10
-2 + 12 = 10
10 = 10
The equation holds true when we substitute x=-2 and y=6 into the first equation.
Now let's plug in (-2, 6) into the second equation 3x + y = 0:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
The equation also holds true when we substitute x=-2 and y=6 into the second equation.
Since (-2, 6) satisfies both equations in the system, it is indeed a solution to the system of linear equations x + 2y = 10 and 3x + y = 0.