toadster77
Answered

Which is the best variable to solve for, and from which equation?

[tex]\[
\begin{array}{l}
3x + 6y = 9 \\
2x - 10y = 13
\end{array}
\][/tex]

A. [tex]$x$[/tex], in the first equation
B. [tex]$y$[/tex], in the second equation
C. [tex]$y$[/tex], in the first equation
D. [tex]$x$[/tex], in the second equation



Answer :

GinnyAnswer
To determine the best variable to solve for and from which equation, let's carefully analyze the given system of equations:

[tex]\[ \begin{array}{l} 3x + 6y = 9 \\ 2x - 10y = 13 \end{array} \][/tex]

### Option A: Solve for [tex]\( x \)[/tex] in the first equation

Starting with the first equation:
[tex]\[ 3x + 6y = 9 \][/tex]

To solve for [tex]\( x \)[/tex]:
[tex]\[ 3x = 9 - 6y \][/tex]
[tex]\[ x = \frac{9 - 6y}{3} \][/tex]

This simplifies to:
[tex]\[ x = 3 - 2y \][/tex]

The solution for [tex]\( x \)[/tex] in the first equation is relatively straightforward.

### Option B: Solve for [tex]\( y \)[/tex] in the second equation

Starting with the second equation:
[tex]\[ 2x - 10y = 13 \][/tex]

To solve for [tex]\( y \)[/tex]:
[tex]\[ -10y = 13 - 2x \][/tex]
[tex]\[ y = \frac{13 - 2x}{-10} \][/tex]

This simplifies to:
[tex]\[ y = -\frac{13}{10} + \frac{1}{5}x \][/tex]

The solution for [tex]\( y \)[/tex] involves dealing with a negative fraction and may be considered a bit more complex.

### Option C: Solve for [tex]\( y \)[/tex] in the first equation

Starting with the first equation:
[tex]\[ 3x + 6y = 9 \][/tex]

To solve for [tex]\( y \)[/tex]:
[tex]\[ 6y = 9 - 3x \][/tex]
[tex]\[ y = \frac{9 - 3x}{6} \][/tex]

This simplifies to:
[tex]\[ y = \frac{3 - x}{2} \][/tex]

The solution for [tex]\( y \)[/tex] in the first equation is also straightforward with simple fractions.

### Option D: Solve for [tex]\( x \)[/tex] in the second equation

Starting with the second equation:
[tex]\[ 2x - 10y = 13 \][/tex]

To solve for [tex]\( x \)[/tex]:
[tex]\[ 2x = 13 + 10y \][/tex]
[tex]\[ x = \frac{13 + 10y}{2} \][/tex]

This simplifies to:
[tex]\[ x = \frac{13}{2} + 5y \][/tex]

Among these options, solving for [tex]\( x \)[/tex] in the first equation looks to involve fewer steps and simpler fractions compared to the other options.

Thus, the best option is:

### A. [tex]\( x \)[/tex], in the first equation.

Other Questions