Question

a system of equations is shown.$\begin{cases} 4x + 10y = 13 \\ 3x + 5y = 14 end{cases}$which method could be used to eliminate a variable from the system?show hints$\bigcirc$ multiply the second equation by $-3$, and then add the equations.$\bigcirc$ multiply the first equation by $-5$, and then add the equations.$\bigcirc$ multiply the first equation by $-3$, and then add the equations.$\bigcirc$ multiply the second equation by $-2$, and then add the equations.

Explanation:

Step1: Analyze y coefficients

First equation: $10y$, second: $5y$.

Step2: Test option 4

Multiply second eq by $-2$:
$-2*(3x + 5y) = -2*14$
$\implies -6x -10y = -28$

Step3: Add to first equation

$(4x + 10y) + (-6x -10y) = 13 + (-28)$
$\implies -2x = -15$ (y is eliminated)

Step4: Verify other options

• Option1: Multiply second by $-3$: $-9x-15y=-42$, add to first: $-5x-5y=-29$ (no elimination)
• Option2: Multiply first by $-5$: $-20x-50y=-65$, add to second: $-17x-45y=-51$ (no elimination)
• Option3: Multiply first by $-3$: $-12x-30y=-39$, add to second: $-9x-25y=-25$ (no elimination)

Answer:

Multiply the second equation by $-2$, and then add the equations.