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Solve the following system of equations:

[tex]\[ \left\{ \begin{array}{l}
2x + y = 4 \\
x + y = -2
\end{array} \right. \][/tex]


Sagot :

To solve the given system of linear equations step-by-step, we have:

[tex]\[ \begin{cases} 2x + y = 4 \quad \text{(1)} \\ x + y = -2 \quad \text{(2)} \\ \end{cases} \][/tex]

Step 1: Subtract Equation (2) from Equation (1). This will eliminate [tex]\( y \)[/tex] and allow us to solve for [tex]\( x \)[/tex].

[tex]\[ (2x + y) - (x + y) = 4 - (-2) \][/tex]

Simplify the left-hand side:

[tex]\[ 2x + y - x - y = 4 + 2 \][/tex]

This reduces to:

[tex]\[ x = 6 \][/tex]

So, we have found that:

[tex]\[ x = 6 \][/tex]

Step 2: Substitute [tex]\( x = 6 \)[/tex] into Equation (2) to solve for [tex]\( y \)[/tex].

Recall Equation (2):

[tex]\[ x + y = -2 \][/tex]

Substitute [tex]\( x = 6 \)[/tex]:

[tex]\[ 6 + y = -2 \][/tex]

Solving for [tex]\( y \)[/tex]:

[tex]\[ y = -2 - 6 \][/tex]

[tex]\[ y = -8 \][/tex]

So, we have found that:

[tex]\[ y = -8 \][/tex]

Conclusion: The solution to the system of equations is:

[tex]\[ (x, y) = (6, -8) \][/tex]

So, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations are:

[tex]\[ x = 6 \quad \text{and} \quad y = -8 \][/tex]
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