Question

Frank solves the system of equations using the linear combination method. 2x+3y=−1

3x−5y=10

Which steps would allow him to eliminate the y terms in the system of equations?


Multiply 2x+3y=−1 by 3. Multiply 3x−5y=10 by 5. Add the resulting equations together.


Multiply 2x+3y=−1 by 3. Multiply 3x−5y=10 by 2. Add the resulting equations together.


Multiply 2x+3y=−1 by 2. Multiply 3x−5y=10 by 5. Add the resulting equations together.


Multiply 2x+3y=−1 by 5. Multiply 3x−5y=10 by 3. Add the resulting equations together.

Answer 1

Multiply 2x + 3y = −1 by 5. Multiply 3x − 5y = 10 by 3. Add the resulting equations together.

Explanation:

To eliminate the y-term. we must multiply both equations by values that make the coefficients of y opposite in sign.

2x + 3y = -1 (1)

3x - 5y = 10 (2)

The easiest way to do this is to multiply Equation (1) by 5

and Equation (2) by 3.

5 × [2x + 3y = -1]

3 × [3x - 5y = 10]

Then, add the two equations.

10x + 15y = -5

9x - 15y = 30

19x = 25

Conclusion: Multiply 2x + 3y = −1 by 5. Multiply 3x − 5y = 10 by 3. Add the resulting equations together.