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 (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 Multiply equation ii by 2 and multiply equation i by -2
The best way to begin solving the system by elimination is by multiplying equation i by 2 and multiplying equation ii by 3.
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 given system of equations by elimination, the idea is to manipulate the equations in such a way that when you add or subtract them, one of the variables will be eliminated. Here is the system of equations given:
i. 2x + y = -3
ii. 3x - 2y = 2
To begin the elimination process, we need to choose a variable to eliminate. In this case, it's best to eliminate the y variable. Now, let's consider the given answer choices:
i. Multiply equation i by 2 and multiply equation ii by 3
ii. Multiply equation ii by 2
iii. Multiply equation i by 2
iv. Multiply equation ii by 2 and multiply equation i by -2
The correct answer is:
iii. Multiply equation i by 2
Explanation:
We choose option iii because if we multiply equation i by 2, it will allow us to easily eliminate the y variable by adding or subtracting. Let's perform the multiplication:
2 * (2x + y) = 2 * (-3)
4x + 2y = -6
Now, we have the equations:
iii. 4x + 2y = -6
ii. 3x - 2y = 2
By adding these two equations, the y variable will be eliminated:
(4x + 2y) + (3x - 2y) = -6 + 2
7x = -4
Now, we can continue solving the system using the resulting equation.