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. 3х - 2y = 2
A. Multiply equation i by 2 and multiply equation i by 3
B. Multiply equation. ii by 2
C. Multiply equation i by 2
D. Multiply equation ii by 2 and multiply equation i by -2
The best way to begin solving the system by elimination is to choose the steps that will result in the coefficients of one of the variables being equal in both equations.
In this case, if we multiply equation i by 2, we will have:
2(2x + y) = 2(-3)
4x + 2y = -6
Now, the coefficient of the y variable in both equations is 2.
Therefore, the best way to begin would be to select option C. Multiply equation i by 2.
To solve the system of equations by elimination, the best way to begin is to multiply equation ii by 2. Therefore, the correct answer is:
B. Multiply equation ii by 2
To solve the system of equations by elimination, you want to manipulate the equations in a way that allows you to eliminate one variable when you add or subtract the equations together.
Let's go through each option and see which one is the best way to begin:
A. Multiply equation i by 2 and multiply equation ii by 3
If you multiply equation i by 2, you will get:
4x + 2y = -6
If you multiply equation ii by 3, you will get:
9x - 6y = 6
In this case, multiplying both equations by different values does not help with elimination, so this option is not the best way to begin.
B. Multiply equation ii by 2
If you multiply equation ii by 2, you will get:
6х - 4y = 4
Multiplying equation ii by 2 does not directly help with elimination, so this option is not the best way to begin.
C. Multiply equation i by 2
If you multiply equation i by 2, you will get:
4x + 2y = -6
Multiplying equation i by 2 allows you to have a coefficient of 2 in front of the y term, which can be directly eliminated when added to equation ii. This option is a good way to begin solving the system by elimination.
D. Multiply equation ii by 2 and multiply equation i by -2
If you multiply equation ii by 2, you will get:
6х - 4y = 4
If you multiply equation i by -2, you will get:
-4x - 2y = 6
Multiplying both equations by different values does not directly help with elimination, so this option is not the best way to begin.
Therefore, the best way to begin solving the system of equations by elimination would be to multiply equation i by 2. So the correct answer is option C: Multiply equation i by 2.