To solve the system using elimination, we want to eliminate one variable by adding or subtracting the two equations. To do this, we need to make sure that the coefficients of one of the variables are the same (or opposite) in both equations.
In this case, to eliminate the x-variable, we should start by multiplying both sides of equation i by 3 and equation ii by 2. This will give us equivalent equations with opposite coefficients for the x-variable:
i. 6x + 3y = -9
ii. 6x - 4y = 4
Now, we can subtract equation ii from equation i to eliminate the x-variable:
(6x + 3y) - (6x - 4y) = -9 - 4
Simplifying,
6x - 6x + 3y + 4y = -13
7y = -13
And if we solve for y, we find that y = -13/7.
Therefore, the best way to begin is by multiplying both sides of equation i by 3 and equation ii by 2.
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 answer