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 correct step to begin solving the system by elimination is to multiply equation i by 2 and equation ii by 3.
The best way to eliminate the variable x is to make the coefficients of x in both equations the same, but with opposite signs. This can be achieved by multiplying equation i by 2 and equation ii by 3.
So, the correct answer is:
A. Multiply equation i by 2 and multiply equation ii by 3.
To solve the system of equations by elimination, we want to multiply one or both of the equations by a constant value to make the coefficients of one of the variables the same or opposite. This will allow us to add or subtract the equations to eliminate that variable.
In this case, looking at the coefficient of the x term, we see that it is already the same in both equations. However, the coefficients of the y term are different (1 in equation i and -2 in equation ii). To eliminate the y variable, we need to make the coefficients the same or opposite.
Since we want to eliminate the y variable, the best way to begin is to multiply equation i by 2 and equation ii by -2. This will give us:
i. 4x + 2y = -6
ii. -6x + 4y = -4
Now, the coefficients of the y term are -2 and 4, which are opposites. We can then proceed to add the equations together to eliminate the y variable.
Therefore, the correct answer is D. Multiply equation ii by 2 and multiply equation i by -2.
To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the two equations. Looking at the given system:
i. 2x + y = -3
ii. 3х - 2y = 2
We can see that the coefficients of y in both equations are already the same (y in equation i and -2y in equation ii), so it would be most efficient to eliminate the x variable.
To do this, we need to make the coefficients of x in both equations the same, but with opposite signs. Comparing the coefficients of x in the two equations, we see that 2 and 3 have a common multiple of 6 (-2 * 3 = -6 and 3 * 2 = 6).
So, the best way to begin would be to multiply equation i by 3 and multiply equation ii by 2.
Therefore, the correct answer is option D: Multiply equation ii by 2 and multiply equation i by -2.