Question

Which of these strategies would eliminate a variable in the system of equations?

Answer 1

Answer:

Option A: Multiply the top equation by $\frac{\textbf{1}}{\textbf{2}}$, then add the equations.

Step-by-step explanation:

OPTION A:

When we multiply the top equation by $\frac{1}{2}$ we get:

$\frac{1}{2}10x + \frac{1}{2}4y = \frac{1}{2}(-2)$

$= 5x + 2y = -1$

Now, we add the second equation to this, we get:

5x + 2y + 5x - 2y = -1 + 2

$\implies 10x = 1$

The 'y' variable is eliminated.

OPTION B: Note that multiplying the second equation by 2 would result in:

10x - 4y = 4. To eliminate 'y' we should add this equation to the top equation not subtract it. So, this option is wrong.

OPTION C:

Adding the equations also will result in a equation of two variables, viz:

15x + 2y = 0 which does not eliminate any variable at all.

So, OPTION C is also wrong.

Hence, OPTION A is the answer.