# Intermediate Algebra (Math)

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Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

-2x Ð 8y = 22

-6x Ð y = 20

At first I tried to multiply by 8 but that did not work.

• Intermediate Algebra (Math) -

I assume the illegible sign is a + sign, since the - sign shows clearly.

-2x + 8y = 22 ....(1)
-6x + y = 20 ....(2)

First, we determine if the system has 0 solution, one solution or many solutions.

Calculate the determinant of the left-hand-side:
Δ=(-2)(1)-(-6)(8)=46
Since Δ≠0, the system has one solution. Multiplying 3*(-1) and add to (2) gives
-23y=-46
solving for y gives
y=2
Substitute y=2 into either (1) or (2) to solve for x.
Then substitute both x and y in the remaining equation for a check.

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