Explanation:
To find the solution to the system of equations, let's substitute the given values for x and y into each equation and determine if they satisfy both equations:
Substituting (5, -3) into the equations:
1) y = -2x + 9
-3 = -2(5) + 9
-3 = -10 + 9
-3 = -1
2) 4x + 2y = 18
4(5) + 2(-3) = 18
20 - 6 = 18
14 = 18
The values (5, -3) do not satisfy the system of equations.
Substituting (-5, 19) into the equations:
1) y = -2x + 9
19 = -2(-5) + 9
19 = 10 + 9
19 = 19
2) 4x + 2y = 18
4(-5) + 2(19) = 18
-20 + 38 = 18
18 = 18
The values (-5, 19) satisfy the system of equations.
Substituting (4, 1) into the equations:
1) y = -2x + 9
1 = -2(4) + 9
1 = -8 + 9
1 = 1
2) 4x + 2y = 18
4(4) + 2(1) = 18
16 + 2 = 18
18 = 18
The values (4, 1) satisfy the system of equations.
Substituting (6, 0) into the equations:
1) y = -2x + 9
0 = -2(6) + 9
0 = -12 + 9
0 = -3
2) 4x + 2y = 18
4(6) + 2(0) = 18
24 + 0 = 18
24 = 18
The values (6, 0) do not satisfy the system of equations.
Therefore, the only solution to the system of equations is (4, 1).