Answer: No, the system of equations has the solution x = 2, y = 1.
So these are the equations
3y=1+x
y=-2x+5
We can substitute “-2x +5” for the y-value because y = -2x +5, so:
3(-2x + 5) = 1 + x
Solve for x:
-6x + 15 = 1 + x
7x + 1 = 15
7x = 14
x = 2
Now you use x = 2 in the original equations to find out the y-value solution.
x = 2
3y=1+x
y=-2x+5
3y = 1 + (2)
3y = 3
y = 1
y = -2(2) + 5
y = -4 + 5
y = 1
Check x = 2, y = 1
3y = 1 + x
3(1) = 1 + 2
3 = 3 ✅
y=-2x+5
(1) = -2(2) + 5
1 = -4 + 5
1 = 1 ✅
So this system of equations has the solution x = 2, y = 1 because
(1) when you use x = 2, y = 1, each individual equation is proven to be true,
and (2) this x- and y-value works for *both* equations listed.