Answer:In this case, there is only one solution to the system of equations.
Explanation:
To find the solutions to a system of equations, we need to find the values of the variables that make both equations in the system true at the same time. One way to do this is to solve each equation for one of the variables, and then substitute that expression into the other equation.
For the first equation, y = −1/4x +5, we can rearrange the terms to get x = (4y - 5)/(-1/4).
For the second equation, 4y + x −20 = 0, we can rearrange the terms to get x = -4y + 20.
Substituting the expression for x from the first equation into the second equation, we get:
(-4y + 20) = (4y - 5)/(-1/4)
This simplifies to:
(-4y + 20) = -4(4y - 5)
Which simplifies to:
16y - 80 = -16y + 20
Which simplifies to:
36y = 100
Dividing both sides by 36, we get:
y = 100/36
This simplifies to:
y = 5/2
Substituting this value back into the first equation, we get:
x = (4(5/2) - 5)/(-1/4)
This simplifies to:
x = (-5/2)/(-1/4)
Which simplifies to:
x = -5/2
Therefore, the solution to the system of equations is (x, y) = (-5/2, 5/2).