Answer :
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]
[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]
