To solve this system, you could do the following steps: 3x+4y=48 6x+2y=60 (6 points)
1. Choose the best method to solve by looking at the way the equations are set up for you:_______
Choose a method
1. Graphing
2. Substitution
3. Elimination
2. Using the best method, how could you get the x variables to cancel out?_____
Operation to get the x variables to cancel
1. Multiply the top equation x-2
2. Divide the bottom equation by 2
3. Multiply the bottom equation x 2
4. Divide the top equation by 4
3. After you complete step 2, what would your top equation be?____
Simplified top equation
1. -6x-8y=-96
2. -6x+4y=96
3. x+2y=46
4. 3x+y=30
4. Line them up and add the equations together to get this equation____
After adding the equations
1. 6y=-96
2. 8y = 96
3. -6y=-36
4. -8y=-96
5. Solve for y in the equation you obtained in step 4:______
Solutions for y
1. y = -16
2. y = 12
3. y = 6
4. y = 24
The correct step to solve the system is as follows:
1. Choose the best method to solve by looking at the way the equations are set up for you: Elimination.
2. Using the best method, multiply the top equation by 2 to get the x variables to cancel:
- Top equation: 3x + 4y = 48
- Multiply by 2: 6x + 8y = 96
3. After you complete step 2, your top equation would be: 6x + 8y = 96.
4. Line them up and subtract the equations to eliminate the x variables:
- Top equation: 6x + 8y = 96
- Bottom equation: 6x + 2y = 60
- Subtracting them gives: 6y = 36
Therefore, after subtracting the equations, the resulting equation is: 6y = 36.
1. The best method to solve this system of equations can be determined by looking at the way the equations are set up. In this case, the equations are already in standard form (Ax + By = C), so both substitution and elimination can be used.
2. To get the x variables to cancel out, you can use the elimination method. In this method, you aim to add or subtract the equations in a way that eliminates one of the variables. In this case, multiplying the top equation by 2 or the bottom equation by 2 would eliminate the x variable.
3. After multiplying the top equation by 2, you would get -6x - 8y = -96. So the simplified top equation would be -6x - 8y = -96, which is option 1.
4. To solve the system, you need to add the equations together. So, after adding the equations, you would get -6x - 8y = -96 - 6x + 2y = 60. Simplifying further, you would get -12y = -36, which is option 3.