Question
Studdy Solution
STEP 1
1. We are given a system of 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 methods such as substitution or elimination to solve the system.
STEP 2
1. Choose a method to solve the system of equations.
2. Solve for one variable.
3. Substitute the found value into one of the original equations to find the other variable.
4. Check the solution by substituting both values back into the original equations.
STEP 3
We will use the elimination method to solve the system of equations:
\begin{align*}
6x - 5y &= -75 \quad \text{(Equation 1)} \\
-x - 2y &= -13 \quad \text{(Equation 2)}
\end{align*}
STEP 4
First, we will eliminate by making the coefficients of in both equations equal. Multiply Equation 2 by 6:
\begin{align*}
6x - 5y &= -75 \\
6(-x - 2y) &= 6(-13)
\end{align*}
This gives us:
\begin{align*}
6x - 5y &= -75 \\
-6x - 12y &= -78
\end{align*}
STEP 5
Add the two equations to eliminate :
Simplify:
STEP 6
Solve for by dividing both sides by :
STEP 7
Substitute back into Equation 2 to solve for :
Simplify:
Add 18 to both sides:
Multiply by :
STEP 8
Check the solution by substituting and back into the original equations:
For Equation 1:
Simplify:
True.
For Equation 2:
Simplify:
True.
Both equations are satisfied.
The solution to the system of equations is:
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