Answer:
(-2, 8) does not satisfy any system of the equation. In other words, no system of the equations satisfies the solution as shown in the graph.
Thus, not a single given option of the system of the equations satisfies the solution as shown in the graph.
Explanation:
We know that the point of intersection of two lines on a graph is the solution of the system of equations.
From the graph, it is clear that the two lines intersect at x=-2 and y=8.
Thus, the point of intersection of the two lines is (-2, 8)
Putting the (-2, 8) in the first system of equations
x+2y=10 and x-y = 6
-2+2(8)=10 and -2-8=6
14 = 10 and -10 = 6
L.H.S ≠ R.H.S and L.H.S ≠ R.H.S
L.H.S and R.H.S of both the system of equations are not equal, It means (-2, 8) does not satisfy the system of the equations x+2y=10 and x-y = 6.
Putting the (-2, 8) in the second system of equations
x+2y=6 and x-y = 10
-2+2(8)=6 and -2-8=10
14 = 6 and -10 = 10
L.H.S ≠ R.H.S and L.H.S ≠ R.H.S
L.H.S and R.H.S of both the system of equations are not equal, It means (-2, 8) does not satisfy the system of the equations x+2y=6 and x-y = 10.
Putting the (-2, 8) in the third system of equations
x+y=6 and x-y = 10
-2+8=6 and -2-8=10
6 = 6 and -10 = 10
L.H.S = R.H.S and L.H.S ≠ R.H.S
L.H.S and R.H.S of x-y = 10 is not equal, It means (-2, 8) does not satisfy the system of the equations x+y=6 and x-y = 10.
Putting the (-2, 8) in the second system of equations
x+y=6 and x-2y = 10
-2+8=6 and -2-2(8)=10
14 = 6 and -18 = 10
L.H.S ≠ R.H.S and L.H.S ≠ R.H.S
L.H.S and R.H.S of both the system of equations are not equal, It means (-2, 8) does not satisfy the system of the equations x+y=6 and x-2y = 10.
In a nutshell, (-2, 8) does not satisfy any system of the equation. In other words, no system of the equations satisfies the solution as shown in the graph.
Thus, not a single given option of the system of the equations satisfies the solution as shown in the graph.