A system of equations is shown:
y, equals, 2, x, plus, 5y=2x+5
y, equals, one quarter, x, minus, one quartery=
4
1
x−
4
1
What is the solution of the system?
To find the solution of the system, we need to solve it by setting the two equations equal to each other:
2x + 5y = 2x + 5
1/4x - 1/4y = 4
We can eliminate the y terms by multiplying the second equation by 4:
x - y = 16
Now we have two equations:
2x + 5y = 2x + 5
x - y = 16
Since the x term cancels out in the first equation, we are left with:
5y = 5
Dividing both sides by 5, we find that y = 1.
Substituting this value of y back into the second equation:
x - 1 = 16
Adding 1 to both sides, we find that x = 17.
So the solution of the system of equations is x = 17, y = 1.