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 i by 2 Multiply equation i by 2
Multiply equation i by 2
Multiply equation ii 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.
The best way to begin solving the system by elimination is to 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 variable by manipulating the equations in such a way that when the equations are added or subtracted, one variable cancels out.
In this case, we need to decide whether to multiply equation i by 2 and equation ii by 3, or vice versa.
To make the coefficient of either "x" or "y" the same (or additive inverses of each other), we need to find a common multiple of the coefficients in each equation. Looking at the coefficients, 2 and 3, we notice that their least common multiple is 6.
So, the best way to begin the elimination process would be to multiply equation i by 3 and equation ii by 2.
This would result in:
(iii) 6x + 3y = -9 (multiply equation i by 3)
(iv) 6x - 4y = 4 (multiply equation ii by 2)
Now, we have two equations with the same coefficient for x, which allows us to eliminate the x term by subtracting equation iv from equation iii.
By subtracting the equations, we get:
6x - 6x + 3y - (-4y) = -9 - 4
Simplifying the equation gives us:
7y = -13
Afterwards, we can continue solving for y, substituting its value into one of the original equations to find the value for x.