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Solve the following system of equations:
[tex]\[ \left\{
\begin{array}{l}
x - y = -9 \\
3x + 4y = 8
\end{array}
\right. \][/tex]

Sagot :

GinnyAnswer
Sure! To solve the system of linear equations:

[tex]\[ \left\{ \begin{array}{l} x - y = -9 \\ 3x + 4y = 8 \end{array} \right. \][/tex]

we'll use the substitution or elimination method. Here, I'll demonstrate the substitution method step-by-step:

1. Solve the first equation for one of the variables:

From the first equation [tex]\(x - y = -9\)[/tex], we can solve for [tex]\(x\)[/tex]:

[tex]\[ x = y - 9 \][/tex]

2. Substitute this expression into the second equation:

Now, substitute [tex]\(x = y - 9\)[/tex] into the second equation [tex]\(3x + 4y = 8\)[/tex]:

[tex]\[ 3(y - 9) + 4y = 8 \][/tex]

3. Simplify and solve for [tex]\(y\)[/tex]:

Distribute the 3:

[tex]\[ 3y - 27 + 4y = 8 \][/tex]

Combine like terms:

[tex]\[ 7y - 27 = 8 \][/tex]

Add 27 to both sides:

[tex]\[ 7y = 35 \][/tex]

Divide both sides by 7:

[tex]\[ y = 5 \][/tex]

4. Substitute back to find [tex]\(x\)[/tex]:

Substitute [tex]\(y = 5\)[/tex] back into the expression for [tex]\(x\)[/tex]:

[tex]\[ x = y - 9 = 5 - 9 = -4 \][/tex]

So, the solution to the system of equations is:

[tex]\[ (x, y) = (-4, 5) \][/tex]

This means [tex]\(x = -4\)[/tex] and [tex]\(y = 5\)[/tex].
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