Answered

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Solve the system of equations:
[tex]\[
\left\{
\begin{array}{l}
4x - y = 5 \\
2x + y = 7
\end{array}
\right.
\][/tex]

Sagot :

GinnyAnswer
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]
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