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
2
+
=
−
3
ii. 3x−2y=2
3
−
2
=
2
(1 point)
Responses

Multiply equation i by 2 and multiply equation ii by 3
Multiply equation i by 2 and multiply equation ii by 3

Multiply equation ii by 2
Multiply equation ii by 2

Multiply equation i by 2
Multiply equation i by 2

Multiply equation ii by 2 and multiply equation i by -2
The best way to begin solving the system by elimination would be to "Multiply equation i by 2 and multiply equation ii by 3." This would allow for the coefficients of either the x or the y term to be the same or opposite, making it easier to eliminate one of the variables.
The best way to begin solving the system by elimination would be to "Multiply equation i by 2 and multiply equation ii by 3". This allows for the coefficients of either the x or y terms to be equal or opposite in value, making elimination possible.
To solve the system of equations by elimination, we want to eliminate one of the variables by making the coefficients of that variable in both equations the same or multiples of each other.
In this case, the best way to begin would be to multiply equation i by 2 and equation ii by 3.
This choice, i.e., "Multiply equation i by 2 and multiply equation ii by 3," is the correct option because it will allow us to eliminate the x variable when we add the two equations together. By multiplying equation i by 2 and equation ii by 3, we get:
2(2x + y) = 2(-3) --> 4x + 2y = -6
3(3x - 2y) = 3(2) --> 9x - 6y = 6
Now, we can add these two equations together:
(4x + 2y) + (9x - 6y) = -6 + 6
This will eliminate the variable y when we add the terms with y:
4x + 9x + 2y - 6y = 0
Simplifying the equation:
13x - 4y = 0
So, the correct choice is to "Multiply equation i by 2 and multiply equation ii by 3" to begin solving the system of equations by elimination.