The question presents a system of linear equations:

1. $5x + 3y = 4$
2. $-2x - 8y = 6$

It asks which strategy can be used to eliminate a variable by applying a multiplier to one or both equations and then adding the equations.

Step 1: Analyze the system of equations

To eliminate a variable, we can make the coefficients of either $x$ or $y$ the same in both equations and then add them.

Eliminating $x$:

• The coefficients of $x$ are $5$ and $-2$. To make them the same, we find their least common multiple (LCM), which is 10.
  • Multiply the first equation by 2: $(5x + 3y = 4) \times 2 \rightarrow 10x + 6y = 8$
  • Multiply the second equation by 5: $(-2x - 8y = 6) \times 5 \rightarrow -10x - 40y = 30$

Adding these equations will eliminate $x$.

Eliminating $y$:

• The coefficients of $y$ are $3$ and $-8$. Their LCM is 24.
  • Multiply the first equation by 8: $(5x + 3y = 4) \times 8 \rightarrow 40x + 24y = 32$
  • Multiply the second equation by 3: $(-2x - 8y = 6) \times 3 \rightarrow -6x - 24y = 18$

Adding these equations will eliminate $y$.

Matching to the options:

The correct answer matches "Multiply the first equation by 2 and the second equation by 5. Then add the equations." This strategy eliminates $x$.

Let me know if you'd like further clarification or step-by-step solving of the system!

Questions to Expand:

1. What happens when you eliminate $y$ instead of $x$?
2. How would substitution work for solving this system instead of elimination?
3. Why do we multiply equations to align coefficients for elimination?
4. Can this system be solved graphically, and what does the solution represent?
5. What is the significance of the LCM when choosing multipliers for elimination?

Tip:

When using elimination, always align the coefficients carefully to avoid errors, and double-check the addition step!