Problem

Solve the following system of linear equations using the substitution method: \[\begin{align*} x + 2y &= 7 \\ 3x - y &= 5 \end{align*}\]

Solution

Step 1 :First, isolate \(x\) in the first equation: \[x = 7 - 2y\]

Step 2 :Then substitute \(x\) in the second equation: \[3(7 - 2y) - y = 5\]

Step 3 :Simplify the equation: \[21 - 6y - y = 5\] or \[21 - 7y = 5\]

Step 4 :Rearrange the equation to solve for \(y\): \[7y = 21 - 5\] or \[y = \frac{16}{7}\]

Step 5 :Substitute \(y\) back into the first equation to solve for \(x\): \[x = 7 - 2 \left(\frac{16}{7}\right)\]

Step 6 :Simplify to find the value of \(x\): \[x = 7 - \frac{32}{7}\] or \[x = \frac{49}{7} - \frac{32}{7} = \frac{17}{7}\]

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

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