Question

How can you eliminate the x-terms in this system?​

Answer 1

3 times the second equation, plus the first

Explanation:

You want a strategy for eliminating x-terms in the system of equations ...

• 9x -7y = -3
• -3x +5y = 9

Elimination

You can eliminate x-terms by making their coefficients opposites. We observe that the coefficient of x in the first equation is -3 times the coefficient of x in the second equation.

Multiplying the second equation by 3 will make the x-coefficient -9, the opposite of that in the first equation. Doing that makes the system ...

• 9x -7y = -3
• -9x +15y = 27

Adding these two equations together will eliminate the x-terms:

(9x -7y) +(-9x +15y) = (-3) +(27)

8y = 24 . . . . . . . simplify; x-terms are gone

You can eliminate x-terms by multiplying the second equation by 3, then adding the two equations together.