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
The best way to begin would be to multiply equation ii by 2 and multiply equation i by -2.
To solve the system of equations by elimination, we want to eliminate one variable by manipulating the equations. In this case, the best way to begin is to multiply equation i by 2 and multiply equation ii by 3.
The correct response is:
Multiply equation i by 2 and multiply equation ii by 3
To solve a system of equations by elimination, you want to choose a method that allows you to eliminate one variable when you add or subtract the two equations. In this case, if we carefully choose the coefficients of the variables, we can eliminate the x variable.
To begin, we want to choose two equations that have the same coefficient in front of the x variable or can easily be made to have the same coefficients. Looking at the given system:
i. 2x + y = -3
ii. 3x - 2y = 2
We can see that if we multiply equation i by 3 and equation ii by 2, we will have equations with the same coefficient in front of the x variable, which is 6.
Therefore, the best way to begin is to multiply equation i by 3 and equation ii by 2.
So the correct answer is: Multiply equation i by 3 and multiply equation ii by 2.