Question

The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the y-variable, and what is the solution for this system? x + 3y = 42 2x − y = 14

Answer 1

Given:

The system of equations is

$x+3y=42$       ...(i)

$2x-y=14$        ...(ii)

To find:

The number that must be multiplied with the second equation to eliminate the y-variable.

Solution:

Coefficient of y variable in equation (i) is 3 and in equation (ii) is -1.

To eliminate y-variable the absolute value of coefficients of y-variables should be same.

So, we need to multiply the second equation by 3 to eliminate the y-variable

Multiplying equation (ii) by 3, we get

$6x-3y=42$      ...(iii)

Adding (i) and (iii), we get

$x+3y+6x-3y=42+42$

$7x=84$

Divide both sides by 7.

$x=12$

Put x=12 in (i).

$12+3y=42$

$3y=42-12$

$3y=30$

Divide both sides by 10.

$y=10$

Therefore, x=12 and y=10.

Answer 2

Answer:

Multiply the second equation by 3. The solution is x = 12, y = 10.

Step-by-step explanation:

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