Julie is asked to solve the system below by elimination. Which of the following steps would be the best way to begin?%0D%0A%0D%0A i. 2x+y=−3%0D%0A2%0D%0A%0D%0A+%0D%0A%0D%0A=%0D%0A−%0D%0A3%0D%0A ii. 3x−2y=2%0D%0A3%0D%0A%0D%0A−%0D%0A2%0D%0A%0D%0A=%0D%0A2%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0AMultiply equation i by 2 and multiply equation ii by 3%0D%0AMultiply equation i by 2 and multiply equation ii by 3%0D%0A%0D%0AMultiply equation ii by 2%0D%0AMultiply equation ii by 2%0D%0A%0D%0AMultiply equation i by 2%0D%0AMultiply equation i by 2%0D%0A%0D%0AMultiply 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 given system of equations by elimination, we need to eliminate one of the variables so that we can solve for the other variable. The goal is to manipulate the equations by adding or subtracting them to eliminate one variable at a time.
Looking at the given system:
i. 2x + y = -3 (equation i)
ii. 3x - 2y = 2 (equation ii)
In order to eliminate one of the variables, we can multiply Equation i by 2 or Equation ii by 2. This will allow us to create opposite coefficients for the variable we want to eliminate.
Therefore, the best way to begin is to multiply Equation i by 2 and multiply Equation ii by 3. This will give:
i. 4x + 2y = -6 (multiply equation i by 2)
ii. 9x - 6y = 6 (multiply equation ii by 3)
Now, we can add these two equations together to eliminate the variable "y". Adding the left sides and right sides of the equations, we get:
(4x + 2y) + (9x - 6y) = (-6) + (6)
13x - 4y = 0
At this point, we have eliminated the variable "y". Now we can continue solving the system using other methods such as substitution or further elimination.