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Solve the system of equations:

[tex]\[
\begin{cases}
2x - 5y = 14 \\
x - 3y = 9
\end{cases}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's solve the system of linear equations step by step:

We start with the two equations:
[tex]\[ 2x - 5y = 14 \][/tex]
[tex]\[ x - 3y = 9 \][/tex]

Step 1: Solve the second equation for [tex]\(x\)[/tex] in terms of [tex]\(y\)[/tex]:
[tex]\[ x - 3y = 9 \][/tex]
Add [tex]\(3y\)[/tex] to both sides to isolate [tex]\(x\)[/tex]:
[tex]\[ x = 3y + 9 \][/tex]

Step 2: Substitute [tex]\(x = 3y + 9\)[/tex] into the first equation:
[tex]\[ 2(3y + 9) - 5y = 14 \][/tex]
Distribute the [tex]\(2\)[/tex]:
[tex]\[ 6y + 18 - 5y = 14 \][/tex]

Step 3: Combine like terms:
[tex]\[ y + 18 = 14 \][/tex]

Step 4: Isolate [tex]\(y\)[/tex] by subtracting 18 from both sides:
[tex]\[ y = 14 - 18 \][/tex]
[tex]\[ y = -4 \][/tex]

Step 5: Substitute [tex]\(y = -4\)[/tex] back into the equation [tex]\(x = 3y + 9\)[/tex] to solve for [tex]\(x\)[/tex]:
[tex]\[ x = 3(-4) + 9 \][/tex]
[tex]\[ x = -12 + 9 \][/tex]
[tex]\[ x = -3 \][/tex]

Therefore, the solution to the system of equations is:
[tex]\[ x = -3 \][/tex]
[tex]\[ y = -4 \][/tex]

The solution can be written as the ordered pair [tex]\((-3, -4)\)[/tex].
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