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Slove the system of equations x+2y= -14 and -4x-y=28 by combining the equations

Slove the system of equations x+2y= -14 and -4x-y=28 by combining the equations-example-1
User Kahlia
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Final answer:

To solve the system of equations x + 2y = -14 and -4x - y = 28, we can use the method of elimination by combining the equations. The solution to the system of equations is x = 42 and y = -28.

Step-by-step explanation:

To solve the system of equations x + 2y = -14 and -4x - y = 28, we can use the method of elimination by combining the equations.

To eliminate the y variable, we can multiply the first equation by 4 and the second equation by 2, which gives us:

4(x + 2y) = 4(-14) and 2(-4x - y) = 2(28)

Simplifying these equations, we get:

4x + 8y = -56 and -8x - 2y = 56

Adding these equations together, we eliminate the y variable and get:

-4x + 6y = 0

Now we can solve for x by multiplying this equation by -1/4:

x = (1/4)*(-4x + 6y)

Simplifying further, we get:

x = -1.5y

Substituting this value of x into the first equation, we can solve for y:

-1.5y + 2y = -14

0.5y = -14

y = -28

Now substituting this value of y back into the equation x = -1.5y, we can solve for x:

x = -1.5*(-28)

x = 42

Therefore, the solution to the system of equations is x = 42 and y = -28.

User Ionut Achim
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