Question

1. gracie wants to solve the system of linear equations shown, using substitution.

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$$\begin{cases} 3x + y = 15 \\\\ 5x - 3y = 11 \\end{cases}$$

which is her best first step?

• multiply the first equation by 3.
• solve the first equation for y.
• solve the second equation for y.
• divide the second equation by 3.

Explanation:

Step1: Recall Substitution Method

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Step2: Analyze Each Equation

• The first equation \(3x + y = 15\) can be easily solved for \(y\) (by subtracting \(3x\) from both sides: \(y=15 - 3x\)).
• The second equation \(5x-3y = 11\) would require more steps to solve for \(y\) (like adding \(3y\), subtracting 11, then dividing by 3).
• Multiplying the first equation by 3 or dividing the second by 3 are not typical first steps for substitution (they are more for elimination method).

So the best first step is to solve the first equation for \(y\).

Answer:

Solve the first equation for \( y \). (The option: Solve the first equation for \( y \).)