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 i by 2 and multiply equation ii by 3
B. Multiply equation ii by 2
C. Multiply equation by 2 O
D. Multiply equation ii by 2 and multiply equation i by -2
To solve the system by elimination, the objective is to eliminate one of the variables by manipulating the equations so that when they are added or subtracted, one of the variables cancels out.
Looking at the given equations, the coefficients of the x terms differ by a factor of 3 and the coefficients of the y terms differ by a factor of 2.
Therefore, the best way to begin would be to choose the option that will make the coefficients of the y terms the same.
The option that satisfies this condition is D. Multiply equation ii by 2 and multiply equation i by -2.
Are you sure
I apologize for the mistake in my previous response. I made an error in reading the coefficients of the y terms.
To begin solving the system by elimination, we want to manipulate the equations so that when they are added or subtracted, one of the variables cancels out.
Looking at the given equations, the coefficients of the x terms differ by a factor of 3, and the coefficients of the y terms differ by a factor of 2.
To eliminate the y variable, we can multiply equation i by 2 and equation ii by 3 so that the coefficients of y in both equations become -2y and -6y respectively.
Therefore, the correct option is A. Multiply equation i by 2 and multiply equation ii by 3.
The best way to begin solving the given system of equations by elimination is to multiply equation i by 2 and multiply equation ii by 3.
Therefore, the correct answer is:
A. Multiply equation i by 2 and multiply equation ii by 3
To solve the system of equations by elimination, the goal is to eliminate one of the variables by manipulating the equations. One way to do this is by multiplying one or both equations by a constant so that the coefficients of one of the variables in both equations become additive inverses of each other.
Let's look at the given system of equations:
i. 2x + y = -3
ii. 3x - 2y = 2
To eliminate the y-variable, we need to manipulate the equations so that the coefficients of y in both equations are additive inverses. Looking at the coefficients of y, we have a 1 in equation i and a -2 in equation ii.
The best way to begin is to multiply equation i by 2 and multiply equation ii by 3. This will ensure that the coefficients of y become additive inverses.
Therefore, the correct answer is option A. Multiply equation i by 2 and multiply equation ii by 3.