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
To solve the system of equations using elimination, you want to multiply one or both equations by a constant to get the coefficients of either x or y to be the same or opposite. In this case, the y coefficients are 1 and -2, so we can multiply the first equation by 2 and the second equation by 1 to make the y coefficients the same.
The best way to begin would be to multiply both sides of the first equation by 2:
2(2x + y) = 2(-3)
4x + 2y = -6
Now, we have the two equations as:
4x + 2y = -6
3x - 2y = 2
By multiplying the first equation by 2, we made the y coefficients the same, which allows us to eliminate y when we add the two equations together.
To begin solving the system by elimination, you should choose a variable to eliminate. In this case, it would be best to eliminate the x-terms or the y-terms. To do this, you need to ensure that the coefficients of either the x-terms or the y-terms are the same or multiples of each other.
In the given system:
I. 2x + y = -3
II. 3x - 2y = 2
The best way to begin would be to eliminate the x-terms. To make the coefficients of the x-term the same or multiples of each other, you can multiply equation I by 3 and equation II by 2.
By doing this, the system becomes:
I. 6x + 3y = -9
II. 6x - 4y = 4
Now, you can subtract equation II from equation I to eliminate the x-terms.
To solve the given system of equations by elimination, we need to eliminate one variable by adding or subtracting the equations.
In this case, the coefficients of y in the two equations are 1 and -2. To eliminate y, we need to make the coefficients the same or multiples of each other.
One way to do this is to multiply the first equation by 2 to make the coefficient of y in both equations -2.
So, the best way to begin is to multiply equation I by 2:
2(2x + y) = 2(-3)
4x + 2y = -6
Now, we have the modified equation I: 4x + 2y = -6 and equation II: 3x - 2y = 2.
These two equations have the same coefficient for y, so we can proceed with eliminating y by adding the two equations.