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
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 this system by elimination is to multiply equation i by 2 and multiply equation ii by 3. This will give you the same coefficient for the x term in both equations, which will allow you to eliminate the x term when adding the two equations together.
The best way to begin solving the system by elimination would be to multiply equation i by 2 and multiply equation ii by 3.
To solve the system of equations by elimination, we want to eliminate one of the variables by adding or subtracting the two equations. The goal is to manipulate the equations so that when they are added or subtracted, one of the variables will cancel out.
Looking at the system of equations:
i. 2x + y = -3
ii. 3x - 2y = 2
One way to begin is to multiply equation i by a certain factor and equation ii by a different factor such that the coefficients of one of the variables, either x or y, will be the same, or their multiples will add up to zero when the equations are added or subtracted.
In this case, the best way to begin is to multiply equation ii by 2 and equation i by -2. This will make the coefficients of x in both equations the same but with opposite signs.
So the correct step is:
Multiply equation ii by 2 and multiply equation i by -2.
The modified equations become:
i. -4x - 2y = 6
ii. 6x - 4y = 4
Now you can proceed to add or subtract the equations to eliminate one of the variables.