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

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

Explanation:

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Answer 2

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.