Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin?
i. 2x+y=−3
ii. 3x−2y=2
Responses
Multiply equation i by 2 and multiply equation ii by 3
Multiply equation ii by 2
Multiply equation i by 2
Multiply equation ii by 2 and multiply equation i by -2
The best way to begin solving the system by elimination would be to multiply equation ii by 2 and multiply equation i by -2.
To solve the system of equations by elimination, you want to choose a step that will eliminate one of the variables. In this case, since the coefficients of the x term in both equations are already different, we can eliminate the x variable by multiplying either equation by a number that will make the coefficients of the x terms equal.
To find the best step to begin, we need to determine which option will result in equal coefficients for the x term in both equations.
Option i suggests multiplying equation i by 2 and equation ii by 3. Let's see if this step will give us the desired result.
Multiplying equation i by 2 gives us:
2 * (2x + y) = 2 * (-3)
4x + 2y = -6
Multiplying equation ii by 3 gives us:
3 * (3x - 2y) = 3 * 2
9x - 6y = 6
Now we can see that both equations have a coefficient of 4 for the x term. Therefore, option i is the best way to begin by multiplying equation i by 2 and multiplying equation ii by 3.