Question

which of the following actions would eliminate the variable x when solving this system:
equation i: $-12x - 3y = -123$
equation ii: $-3x + y = -15$
\bigcirc multiply equation ii by 3 and add the equations
\bigcirc multiply equation ii by 4 and add the equations
\bigcirc multiply equation ii by 3 and subtract the equations
\bigcirc multiply equation ii by 4 and subtract the equations

Explanation:

Step1: Check coefficients of x

Equation I: $-12x$; Equation II: $-3x$

Step2: Find multiplier for Equation II

To make $x$ coefficients opposites or equal: $-3x \times 4 = -12x$, same as Equation I's $x$ coefficient

Step3: Verify elimination

Multiply Equation II by 4: $-12x + 4y = -60$. Add to Equation I: $(-12x -3y) + (-12x +4y) = -123 + (-60)$? No, wait—add to eliminate: actually, multiply Equation II by 4 gives $-12x + 4y = -60$, add to Equation I: $(-12x -3y) + (-12x +4y)$ doesn't eliminate x? Wait correction: multiply Equation II by -4: $12x -4y = 60$, add to Equation I: $(-12x -3y)+(12x -4y)=-123+60$ eliminates x. But among options, only multiply II by 4 and add is listed? Wait no, original options: the correct action to eliminate x is to make coefficients of x equal in magnitude opposite in sign. Equation I has -12x, Equation II has -3x. Multiply Equation II by 4: -12x +4y=-60. Then subtract Equation II (new) from Equation I: (-12x-3y)-(-12x+4y)=-123-(-60) → -7y=-63 eliminates x. But the option "Multiply Equation II by 4 and subtract the equations" is present? Wait the options are:

1. Multiply Equation II by 3 and add
2. Multiply Equation II by 4 and add
3. Multiply Equation II by3 and subtract
4. Multiply Equation II by4 and subtract

Ah, correct: multiply II by4: -12x+4y=-60. Subtract from Equation I: (-12x-3y) - (-12x+4y) = -123 - (-60) → -7y=-63 (eliminates x). So the option is "Multiply Equation II by4 and subtract the equations".

(Note: Earlier miscalculation—subtraction eliminates x here. So the correct answer is the option stating multiply II by4 and subtract.)

Answer:

Multiply Equation II by 4 and add the equations