Question
Studdy Solution
STEP 1
1. We are given a system of two linear equations with two variables, and .
2. The goal is to find the values of and that satisfy both equations simultaneously.
3. We can use either the substitution method or the elimination method to solve this system.
STEP 2
1. Choose a method to solve the system of equations.
2. Solve for one variable in terms of the other.
3. Substitute the expression into the other equation.
4. Solve the resulting single-variable equation.
5. Substitute back to find the other variable.
6. Verify the solution by plugging the values back into the original equations.
STEP 3
Choose the elimination method to solve the system of equations.
STEP 4
Multiply the first equation by 3 to eliminate the fraction:
Now the system of equations is:
STEP 5
Subtract the first equation from the second equation to eliminate :
STEP 6
Simplify the equation:
Combine like terms:
STEP 7
Solve for by multiplying both sides by :
STEP 8
Substitute back into the first equation to find :
STEP 9
Verify the solution by substituting and into the original equations:
First equation:
True.
Second equation:
True.
The solution is:
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