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Solución
To solve the system of equations using the elimination method, follow these steps:
Step 1: Align the Equations
First, write the equations clearly:
Step 2: Make the Coefficients of One Variable Opposite
We’ll eliminate
by making the coefficients of
in both equations opposites. To do this, find the Least Common Multiple (LCM) of 9 and 2, which is 18.
-
Multiply Equation 1 by 2:
-
Multiply Equation 2 by 9:
Step 3: Add the Modified Equations
Add Equation 3 and Equation 4 to eliminate
:
Step 4: Solve for
Step 5: Substitute
into One of the Original Equations
Using Equation 1:
Solution:
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Como
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Bonus Knowledge
To use the elimination method, we want to eliminate one of the variables by making the coefficients of that variable the same in both equations. Let’s focus on eliminating
.
First, we can manipulate the coefficients of
in both equations. Multiply the first equation by 2 and the second equation by 9:
-
→ -
→
Now we can add these two equations together:
This simplifies to:
Dividing both sides by -11 gives us:
Now that we have
, we can substitute it back into one of the original equations to find
. Let’s use the first equation:
This simplifies to:
Subtract 8 from both sides:
Dividing both sides by 9 gives us:
Thus, the solution to the system of equations is:
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