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What is the solution to this system of equations?
[tex]\[
\begin{array}{l}
2x + y = 5 \\
x - y = 4
\end{array}
\][/tex]
A. [tex]\((-1, 3)\)[/tex]
B. [tex]\((-3, 1)\)[/tex]
C. [tex]\((3, -1)\)[/tex]
D. [tex]\((1, -3)\)[/tex]

Sagot :

GinnyAnsweridn
To solve the given system of equations:
[tex]\[ \begin{array}{l} 2x + y = 5 \\ x - y = 4 \end{array} \][/tex]

We can start by solving one of the equations for one of the variables and then substitute it into the other equation. Let's work with the second equation to express [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:

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

Next, we substitute [tex]\( x = y + 4 \)[/tex] into the first equation:

[tex]\[ 2(y + 4) + y = 5 \][/tex]

Simplify this equation:

[tex]\[ 2y + 8 + y = 5 \][/tex]
[tex]\[ 3y + 8 = 5 \][/tex]

Subtract 8 from both sides to isolate the term with [tex]\( y \)[/tex]:

[tex]\[ 3y = 5 - 8 \][/tex]
[tex]\[ 3y = -3 \][/tex]

Divide by 3:

[tex]\[ y = -1 \][/tex]

Now that we have the value of [tex]\( y \)[/tex], substitute [tex]\( y = -1 \)[/tex] back into the expression [tex]\( x = y + 4 \)[/tex]:

[tex]\[ x = -1 + 4 \][/tex]
[tex]\[ x = 3 \][/tex]

Thus, the solution to the system of equations is:

[tex]\[ (x, y) = (3, -1) \][/tex]

So, the correct answer from the given options is:

[tex]\[ (3, -1) \][/tex]
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