Question5.
Studdy Solution
STEP 1
1. We are given a system of two linear equations.
2. The goal is to find the values of and that satisfy both equations simultaneously.
3. We will use the substitution method to solve the system.
STEP 2
1. Set the equations equal to each other.
2. Solve for .
3. Substitute the value of back into one of the original equations to find .
4. Verify the solution by checking both equations.
STEP 3
Since both equations are equal to , we can set them equal to each other:
STEP 4
To solve for , first get all terms involving on one side of the equation and constant terms on the other:
STEP 5
Combine like terms:
STEP 6
Divide both sides by to solve for :
STEP 7
Substitute back into one of the original equations to find . We'll use the first equation:
STEP 8
Simplify the equation:
STEP 9
Verify the solution by substituting and into the second equation:
STEP 10
Simplify the equation:
Both sides are equal, confirming our solution is correct.
The solution to the system of equations is:
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