Answer:
(x, -1/2x + 5/2) or infinitely many solutions
Explanation:
We can solve the system of equations using substitution. We can start by isolating x in the first equation. Then, we can plug in the entire equation made from isolating for x in the second equation, which will allow us to find y:
Isolating:
x = -2y + 5
Plugging in and solving for y:
4(-2y + 5) + 8y = 20
-8y + 20 + 8y = 20
20 = 20
We see that we get a constant equal to another constant. Whenever you get this as a solution to a system of equations, this means that there are infinitely many solutions. We can express the general rule for the solution in coordinate form by isolating y in at least one of the equations:
y = -1/2x + 5/2
Thus, the general rule for the solution to the system of equations is
(x, -1/2x + 5/2), so you can either put this general rule as the answer or write solution = infinitely many solutions
You can see that there are infinitely many solutions by plugging in any number for x into the two equations and see that you get 5 for the equation and 20 for the second equation. Let's try 4 for x and 0 for x:
4 for x in first equation:
4 + 2(-1/2(4) + 5/2) = 5
4 + 2(0.5) = 5
4 + 1 = 5
5 = 5
4 for x in the second equation
4(4) + 8(-1/2(4) + 5/2) = 20
16 + 8(0.5) = 20
16 +4 = 20
20 = 20
0 for x in the first equation:
0 + 2(-1/2(0) + 5/2) = 5
0 + 2(2.5) = 5
5 = 5
0 for x in the second equation:
4(0) + 8(-1/2(0) + 5/2) = 20
0 + 8(2.5) = 20
20 = 20