Answer :
Alright, let's solve the system of equations step-by-step. We have the following system:
[tex]\[ \begin{cases} 4x - y = 5 \quad \text{(1)} \\ 2x + y = 7 \quad \text{(2)} \end{cases} \][/tex]
Step 1: Add the two equations together to eliminate \(y\).
[tex]\[ (4x - y) + (2x + y) = 5 + 7 \][/tex]
[tex]\[ 4x - y + 2x + y = 12 \][/tex]
[tex]\[ 6x = 12 \][/tex]
Step 2: Solve for \(x\).
[tex]\[ 6x = 12 \][/tex]
[tex]\[ x = 2 \][/tex]
Step 3: Substitute \(x = 2\) back into one of the original equations to solve for \(y\). We'll use equation (2):
[tex]\[ 2x + y = 7 \][/tex]
[tex]\[ 2(2) + y = 7 \][/tex]
[tex]\[ 4 + y = 7 \][/tex]
[tex]\[ y = 3 \][/tex]
So, the solution to the system of equations is:
[tex]\[ x = 2, \quad y = 3 \][/tex]
[tex]\[ \begin{cases} 4x - y = 5 \quad \text{(1)} \\ 2x + y = 7 \quad \text{(2)} \end{cases} \][/tex]
Step 1: Add the two equations together to eliminate \(y\).
[tex]\[ (4x - y) + (2x + y) = 5 + 7 \][/tex]
[tex]\[ 4x - y + 2x + y = 12 \][/tex]
[tex]\[ 6x = 12 \][/tex]
Step 2: Solve for \(x\).
[tex]\[ 6x = 12 \][/tex]
[tex]\[ x = 2 \][/tex]
Step 3: Substitute \(x = 2\) back into one of the original equations to solve for \(y\). We'll use equation (2):
[tex]\[ 2x + y = 7 \][/tex]
[tex]\[ 2(2) + y = 7 \][/tex]
[tex]\[ 4 + y = 7 \][/tex]
[tex]\[ y = 3 \][/tex]
So, the solution to the system of equations is:
[tex]\[ x = 2, \quad y = 3 \][/tex]
