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Use substitution to solve the system.+−2x5y = −27+2y11 = x

Question

Use substitution to solve the system.+−2x5y = −27+2y11 = x

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Solution 1

Step 1: From the second equation, we have x = 2y + 11.

Step 2: Substitute x = 2y + 11 into the first equation. We get -2(2y + 11) + 5y = -27.

Step 3: Simplify the equation. We get -4y - 22 + 5y = -27.

Step 4: Combine like terms. We get y - 22 = -27.

Step 5: Solve for y. We get y = -27 + 22 = -5.

Step 6: Substitute y = -5 into the second equation. We get x = 2(-5) + 11 = 1.

So, the solution to the system of equations is x = 1, y = -5.

This problem has been solved

Solution 2

Step 1: Identify the equation where one variable is isolated. In this case, it's the second equation: x = 2y + 11.

Step 2: Substitute the expression for x from the second equation into the first equation. This gives us: -2(2y + 11) + 5y = -27.

Step 3: Simplify the equation. This gives us: -4y - 22 + 5y = -27.

Step 4: Combine like terms. This gives us: y - 22 = -27.

Step 5: Solve for y by adding 22 to both sides of the equation. This gives us: y = -5.

Step 6: Substitute y = -5 into the second equation to solve for x. This gives us: x = 2(-5) + 11 = 1.

So, the solution to the system of equations is x = 1, y = -5.

This problem has been solved

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