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:
- In this case, the best method would be elimination.
2. Using the best method, how could you get the x variables to cancel out?
- By multiplying the first equation by 2 and the second equation by -3, the x variables will cancel out.
3. After you complete step 2, what would your top equation be?
- The top equation after elimination would be 6x + 8y = 96.
4. Line them up and add the equations together to get this equation.
- After adding the equations, we get 0 + 12y = 156.
5. Solve for y.
- Dividing both sides of the equation by 12, we have y = 13.
6. Solve for x.
- Plugging the value of y into either of the original equations, we can solve for x. Let's use the first equation:
3x + 4y = 48
3x + 4(13) = 48
3x + 52 = 48
3x = 48 - 52
3x = -4
x = -4/3
1. The best method to solve this system of equations is substitution.
2. To get the x variables to cancel out, we need to solve one of the equations for x or y in terms of the other variable. Let's solve the first equation for x:
3x + 4y = 48
3x = 48 - 4y
x = (48 - 4y)/3
3. After completing step 2, the top equation becomes:
x = (48 - 4y)/3
4. Line up the new top equation with the second equation and add them together:
x + 6x + 2y = (48 - 4y)/3 + 6x + 2y = 60
5. Simplify the equation obtained in step 4 and solve for y:
(48 - 4y)/3 + 6x + 2y = 60
(48 - 4y)/3 + 2y = 60 - 6x
(48 - 4y + 6y)/3 = 60 - 6x
(48 + 2y)/3 = 60 - 6x
48 + 2y = 3(60 - 6x)
48 + 2y = 180 - 18x
2y = 180 - 18x - 48
2y = 132 - 18x
y = (132 - 18x)/2
6. Now that we have obtained the value of y, we can substitute it back into one of the original equations to solve for x. Let's substitute it into the first equation:
3x + 4((132 - 18x)/2) = 48
3x + 2(132 - 18x) = 48
3x + 264 - 36x = 48
-33x + 264 = 48
-33x = 48 - 264
-33x = -216
x = (-216)/(-33)
x = 6.545
Therefore, the solution to the system of equations is x ≈ 6.545 and y = (132 - 18x)/2.
1. The best method to solve this system of equations is by using the method of elimination. Since the coefficients of the y variable in both equations are different, eliminating the x variable would be more straightforward in this case.
2. To get the x variables to cancel out, we can multiply the first equation by 2 and the second equation by -3. This will give us:
Equation 1: 6x + 8y = 96
Equation 2: -18x - 6y = -180
3. After completing step 2, the top equation would be: 6x + 8y = 96.
4. To add the equations together and eliminate the x variable, we can simply add Equation 1 and Equation 2:
(6x + 8y) + (-18x - 6y) = 96 + (-180)
-12x + 2y = -84
5. Now, we can solve for y by isolating the y variable in the equation -12x + 2y = -84:
2y = -12x - 84
y = (-12x - 84) / 2
y = -6x - 42
6. To solve for x, we can substitute the value of y = -6x - 42 into one of the original equations:
3x + 4(-6x - 42) = 48
3x - 24x - 168 = 48
-21x = 216
x = -216 / -21
x = 10.2857 (rounded to 4 decimal places)
Therefore, the solution to the system of equations is x = 10.2857 and y = -6(10.2857) - 42.