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What is the solution to the system of equations?

[tex]\[
\begin{array}{l}
y = 2x - 3.5 \\
x - 2y = -14
\end{array}
\][/tex]

A. [tex]\((-7, 3.5)\)[/tex]

B. [tex]\((3.5, -7)\)[/tex]

C. [tex]\((7, 10.5)\)[/tex]

D. [tex]\((10.5, 7)\)[/tex]

Sagot :

GinnyAnsweridn
To solve the system of equations given by:
[tex]\[ \begin{cases} y = 2x - 3.5 \\ x - 2y = -14 \end{cases} \][/tex]

we can follow these steps:

1. Write down the first equation:
[tex]\[ y = 2x - 3.5 \][/tex]

2. Substitute the expression for [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ x - 2(2x - 3.5) = -14 \][/tex]

3. Expand and simplify the equation:
[tex]\[ x - 4x + 7 = -14 \][/tex]
[tex]\[ -3x + 7 = -14 \][/tex]

4. Isolate the [tex]\( x \)[/tex] term by subtracting 7 from both sides:
[tex]\[ -3x = -21 \][/tex]

5. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = 7 \][/tex]

6. Substitute this value of [tex]\( x \)[/tex] back into the first equation to solve for [tex]\( y \)[/tex]:
[tex]\[ y = 2(7) - 3.5 \][/tex]
[tex]\[ y = 14 - 3.5 \][/tex]
[tex]\[ y = 10.5 \][/tex]

So, the solution to the system of equations is [tex]\((7, 10.5)\)[/tex].

Therefore, the correct answer from the given options is:
[tex]\[ (7, 10.5) \][/tex]
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