Problem

Solve the following system of equations with the substitution method: \[ \left\{\begin{array}{l} x+3 y=-1 \\ -3 x-4 y=5 \end{array}\right. \] Answer: $(x, y)=$ Preview $x$ : Preview $y$ : Enter your answers as integers or as reduced fractions in the form A/B.

Solution

Step 1 :First, we solve the first equation for x: \(x = -3y - 1\)

Step 2 :Next, we substitute this expression for x into the second equation: \(-3(-3y - 1) - 4y = 5\)

Step 3 :Solving this equation gives us \(y = \frac{2}{5}\)

Step 4 :Substituting \(y = \frac{2}{5}\) back into the first equation gives us \(x = -\frac{11}{5}\)

Step 5 :\(\boxed{(x, y) = \left(-\frac{11}{5}, \frac{2}{5}\right)}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8793/

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