To solve this system, you could do the following steps:
3x+4y=48
6x+2y=60
1. Choose the best method to solve by looking at the way the equations are set up for you: ___
2. Using the best method, how could you get the x variables to cancel out? ____
3. After you complete step 2, what would your top equation be? ____
4. Line them up and add the equations together to get this equation. _____
5. Solve for y. ____
6. Solve for x. _____
1. Choose the best method to solve by looking at the way the equations are set up for you: One possible method is the method of substitution, as one of the equations can easily be solved for one variable.
2. Using the best method, how could you get the x variables to cancel out? We can multiply the second equation by (-3) and the first equation by 2, which will give us -18x in both equations, allowing us to cancel out the x variable.
3. After you complete step 2, what would your top equation be? The top equation would be -18x - 6y = -180.
4. Line them up and add the equations together to get this equation. -18x - 6y + 6x + 8y = -180 + 48.
5. Solve for y. Simplifying the equation from step 4, we get -12x + 2y = -132. From this equation, we can solve for y by isolating it and simplifying: 2y = -12x - 132, y = -6x - 66.
6. Solve for x. We can substitute the expression for y from step 5 into one of the original equations. Let's use the first equation: 3x + 4(-6x - 66) = 48. Solving for x, we get x = 6.
Therefore, the solution to the system of equations is x = 6 and y = -6(6) - 66 = -102.
The answer options for each section were:
Section one: Graphing, Substitution, or Elimination
Section two: Divide the top equation by 4, Multiply the tope equation x -2, Divide the bottom equation by 2, Multiply the bottom equation x 2
Section three: 3x+y=30, -6x-8y=-96, -6x+4y=96, x+2y=46
Section four: -8y=-96, 6y=-96, 8y=96, -6y=-36
Section five: y=-12, y=18, y=6
Section six: x=8, x=-3, x=6
1. Choose the best method to solve by looking at the way the equations are set up for you: The best method would be substitution since one equation can be easily solved for one variable.
2. Using the best method, how could you get the x variables to cancel out? Divide the top equation by 4.
3. After you complete step 2, what would your top equation be? The top equation would be x - 2y = 12.
4. Line them up and add the equations together to get this equation. -6x + 2y = 60.
5. Solve for y. Simplifying the equation from step 4, we get -6x + 4y = 60. From this equation, we can solve for y by isolating it and simplifying: 4y = 6x + 60, y = (6/4)x + 15/2.
6. Solve for x. We can substitute the expression for y from step 5 into one of the original equations. Let's use the first equation: 3x + 4((6/4)x + 15/2) = 48. Solving for x, we get x = 8/3.
Therefore, the solution to the system of equations is x = 8/3 and y = (6/4)(8/3) + 15/2, which simplifies to x = 8/3 and y = 6.
are you sure?
I apologize for the incorrect response. Let's go through the steps again:
1. Choose the best method to solve by looking at the way the equations are set up for you: The best method would be elimination since the coefficients of x or y can be easily made equal or opposite by multiplying or dividing.
2. Using the best method, how could you get the x variables to cancel out? Multiply the top equation by -2.
3. After you complete step 2, what would your top equation be? The top equation would be -6x - 8y = -96.
4. Line them up and add the equations together to get this equation. (-6x - 8y) + (6x + 2y) = -96 + 60.
5. Solve for y. Simplifying the equation from step 4, we get -6y = -36. Solving for y, we get y = 6.
6. Solve for x. We can substitute the value of y into one of the original equations to solve for x. Let's use the first equation: 3x + 4(6) = 48. Solving for x, we get x = 8.
Therefore, the solution to the system of equations is x = 8 and y = 6. Once again, I apologize for the earlier confusion.
Can you simplify step 4 so it is one of my answer choices that I listed
Apologies for the confusion. Let's go through the steps again:
1. Choose the best method to solve by looking at the way the equations are set up for you: The best method would be elimination since the coefficients of x or y can be easily made equal or opposite by multiplying or dividing.
2. Using the best method, how could you get the x variables to cancel out? Multiply the bottom equation by 2.
3. After you complete step 2, what would your top equation be? The top equation would be 3x + 4y = 48.
4. Line them up and add the equations together to get this equation. (3x + 4y) + (6x + 2y) = 48 + 60.
5. Solve for y. Simplifying the equation from step 4, we get 9x + 6y = 108. Solving for y, we get 6y = -9x + 108, y = (-3/2)x + 18.
6. Solve for x. We can substitute the expression for y from step 5 into one of the original equations. Let's use the first equation: 3x + 4[(-3/2)x + 18] = 48. Solving for x, we get x = 8.
Therefore, the solution to the system of equations is x = 8 and y = (-3/2)(8) + 18, which simplifies to x = 8 and y = 6.