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 2 + = − 3 ii. 3x−2y=2 3 − 2 = 2
To solve the system by elimination, we need to eliminate one of the variables by adding or subtracting the two equations.
In this case, the best way to begin would be to multiply both sides of the first equation (i) by 2. This will allow us to eliminate the variable "y" when we add the two equations together.
So, the best way to begin is:
ii. Multiply equation (i) by 2: 2(2x+y) = 2(-3), which simplifies to 4x+2y = -6
To solve the system using elimination, we want to eliminate one variable by adding or subtracting the two equations. To do this, we need to make sure that the coefficients of one of the variables are the same (or opposite) in both equations.
In this case, to eliminate the x-variable, we should start by multiplying both sides of equation i by 3 and equation ii by 2. This will give us equivalent equations with opposite coefficients for the x-variable:
i. 6x + 3y = -9
ii. 6x - 4y = 4
Now, we can subtract equation ii from equation i to eliminate the x-variable:
(6x + 3y) - (6x - 4y) = -9 - 4
Simplifying,
6x - 6x + 3y + 4y = -13
7y = -13
And if we solve for y, we find that y = -13/7.
Therefore, the best way to begin is by multiplying both sides of equation i by 3 and equation ii by 2.
To solve the system of equations by elimination, we want to eliminate one of the variables by adding or subtracting the equations. Let's analyze the given system:
i. 2x + y = −3
ii. 3x − 2y = 2
To determine the best way to begin, we need to observe the coefficients of the variables. In this case, the coefficients of x in each equation are different, while the coefficients of y are the same.
To eliminate one of the variables, we can multiply both sides of equation i by 2, which will make the coefficients of y in both equations equal and opposite. This way, when we add the equations together, the y term will cancel out.
Steps to begin:
1. Multiply equation i by 2:
2(2x + y) = 2(−3)
This simplifies to:
4x + 2y = −6
2. Now we have two equations:
4x + 2y = −6 (equation iii, after multiplying equation i by 2)
3x − 2y = 2 (equation ii, unmodified)
3. Add the equations together to eliminate the y term:
(4x + 2y) + (3x − 2y) = −6 + 2
This simplifies to:
7x = -4
By performing these steps, we've eliminated the y term and obtained a new equation involving only x. We can now proceed to solve for x.