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
a. Multiply equation 1 by 2 and multiply equation 11 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
To solve the system of equations by elimination, the best way to begin is to multiply equation i by 2 and equation ii by 3.
Therefore, the correct answer is:
a. Multiply equation 1 by 2 and multiply equation ii by 3
The best way to begin solving the system by elimination would be to multiply equation i by 2 and multiply equation ii by 3. Therefore, the correct answer is option a.
To solve the system of equations using elimination, we want to eliminate one variable by multiplying one of the equations so that the coefficients of the variable in both equations will be the same or multiples of each other.
Let's check each option:
a. Multiply equation 1 by 2 and multiply equation 2 by 3: This option would give us:
2(2x+y)=-3(2) => 4x+2y=-6
3(3x-2y)=2(3) => 9x-6y=6
In this case, we don't eliminate any variable, so this option is not the best way to begin.
b. Multiply equation 2 by 2: This option would give us:
2(3x-2y)=2(2) => 6x-4y=4
Here, we do not obtain coefficients that can be eliminated. Hence, this option is not the best way to begin either.
c. Multiply equation 1 by 2: This option would give us:
2(2x+y)=-3(2) => 4x+2y=-6
By multiplying equation 1 by 2, we obtain coefficients that can be eliminated (2y in this case). Hence, this option is a good way to begin eliminating one variable from the system.
d. Multiply equation 2 by 2 and multiply equation 1 by -2: This option would give us:
-2(2x+y)=-2(-3) => -4x-2y=6
2(3x-2y)=2(2) => 6x-4y=4
By multiplying equation 2 by 2 and equation 1 by -2, we again obtain coefficients that can be eliminated (2y in this case). Hence, this option is also a good way to begin eliminating one variable from the system.
Comparing options (c) and (d), both will lead to the elimination of the same variable, so either option can be chosen as the best way to begin. However, the specific steps after this initial elimination may differ based on the chosen option.
Therefore, the best way to begin solving the system by elimination is either option c or option d.