Question

How many solutions does the system of equations have?

y=−2x+12
4y+x−20=0

Answer 1

To find the number of solutions for the system of equations, we can solve them to determine if they intersect at a single point (1 solution), parallel lines (no solution), or coincident lines (infinitely many solutions).

We'll start by rearranging the second equation to isolate x:
4y + x - 20 = 0
x = 20 - 4y

Now we substitute this expression for x into the first equation:
y = -2x + 12
y = -2(20 - 4y) + 12
y = -40 + 8y + 12
-7y = -28
y = 4

Finally, we substitute this value of y into the expression we found for x:
x = 20 - 4y
x = 20 - 4(4)
x = 4

Therefore, the system of equations has a unique solution, which is (4, 4).