Final answer:
To produce opposite coefficients for y in the given equations, multiply the first equation by 7 and the second by 8. This will result in opposite y coefficients of -7 and +7, allowing their elimination when the equations are added together.
Step-by-step explanation:
To solve the system of equations by producing opposite coefficients for x or y, we need to select appropriate multipliers for each equation to ensure that when we add or subtract the equations, one of the variables will be eliminated. Looking at the given equations:
- 1x - 1y = 100
- 3/8x + 7/8y = 2000
We want to find multipliers for x or y that produce opposite coefficients. To do this, observe that the coefficient of y in the first equation is -1 and the coefficient of y in the second equation is 7/8. Therefore, we can multiply the first equation by 7 and the second equation by 8 to obtain opposite coefficients of y. Doing this gives us:
- 7(1x - 1y) = 7×100
- 8(3/8x + 7/8y) = 8×2000
Which simplifies to:
- 7x - 7y = 700
- 3x + 7y = 16000
Now, by adding these two equations, the y terms will cancel out since they have opposite coefficients (-7y and +7y).