Question
A system of equations is given.
Equation 1:5x-2y=10
Equation
Explain how to eliminate
in the system of equations.
Equation 1:5x-2y=10
Equation
Explain how to eliminate
Ask by Fernandez Sherman. in the United States
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
To eliminate
, multiply the first equation by 4 and the second by 5 to make the coefficients of
equal. Then subtract the second equation from the first to cancel
, solving for
.
Solution

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Beyond the Answer
To eliminate
in the system of equations, you’ll want to manipulate the equations so that the coefficients of
in both equations match. Start by multiplying Equation 1 by 4, resulting in
. For Equation 2, multiply it by 5, leading to
. Now, both equations have the same coefficient for
(20).
Next, subtract the first modified equation from the second:
. This simplifies to
, allowing you to solve for
easily. By finding
, you can substitute it back into one of the original equations to solve for
. Fun fact: you can visualize this process like two dancers in sync, making sure their steps match before they smoothly pull off the next move!
As you dive deeper into this, keep in mind one common pitfall: not aligning the equations properly before elimination. It’s like trying to line up for a group photo with everyone facing different directions—you either end up with a messy shot or, worse, missing someone in the frame! Make those equations uniform before you take your perfect picture of the solution!