QuestionUse the method of elimination to solve the following system of equations. If the system is dependent, express the solution set in terms of one of the variables. Leave all fractional answers in fraction form.
Studdy Solution
STEP 1
1. We are given a system of two linear equations with two variables.
2. The method of elimination involves adding or subtracting equations to eliminate one variable.
3. We will check if the system is independent, dependent, or inconsistent.
STEP 2
1. Align the equations for elimination.
2. Eliminate one variable by adding or subtracting the equations.
3. Solve for the remaining variable.
4. Substitute back to find the other variable.
5. Check if the system is dependent or independent.
STEP 3
Write the given system of equations:
1.
2.
Notice that the coefficients of in both equations are multiples of each other. This suggests we can eliminate by manipulating the equations.
STEP 4
To eliminate , let's multiply the first equation by 3 so that the coefficients of will be opposites:
Multiply equation 1 by 3:
This gives:
Now we have:
1.
2.
STEP 5
Add the two equations together to eliminate :
Simplify:
This is a contradiction, indicating that the system of equations is inconsistent.
STEP 6
Since we obtained a contradiction, the system has no solution. The lines represented by the equations are parallel and do not intersect.
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