To solve this system, you could do the following steps:
3х + 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: _
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. The best method to solve this system of equations is elimination method.
2. To get the x variables to cancel out, we can multiply the first equation by 2 and the second equation by 3.
3. After step 2, the top equation will be: 6x + 8y = 96.
4. Adding the two equations together, we get: (6x + 8y) + (6x + 2y) = 96 + 60, which simplifies to 12x + 10y = 156.
5. To solve for y, we can isolate y in the equation 12x + 10y = 156. Subtracting 12x from both sides, we get 10y = 156 - 12x. Dividing both sides by 10, we have y = (156 - 12x)/10, which can be further simplified if needed.
6. To solve for x, we need to substitute the value of y into either of the original equations. Let's substitute y = (156 - 12x)/10 into the first equation 3x + 4y = 48. This gives us 3x + 4((156 - 12x)/10) = 48. Simplifying and solving for x will give us the value of x.
1. The best method to solve this system of equations depends on the specific situation and personal preference. However, in this case, the elimination method seems appropriate since it involves eliminating one of the variables by adding or subtracting the equations.
2. To get the x variables to cancel out, we need to multiply one or both equations by appropriate numbers so that the coefficients of x in both equations become equal, but with opposite signs. In this case, if we multiply the first equation by -2, the x coefficients will become -6 in both equations.
3. After completing step 2, the top equation will become:
-6x - 8y = -96
4. Line up the equations by stacking them on top of each other, and add them together term by term. The resulting equation will be:
-6x - 8y + 6x + 2y = -96 + 60
5. Simplify the equation and combine like terms:
-6y = -36
6. Solve for y by isolating the variable by dividing both sides of the equation by -6:
y = -36 / -6
y = 6
7. Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
3x + 4(6) = 48
8. Simplify and solve for x:
3x + 24 = 48
3x = 48 - 24
3x = 24
x = 24 / 3
x = 8
Therefore, the solution to the system of equations is x = 8 and y = 6.
1. The best method to solve this system of equations is the method of elimination because the coefficients of one variable in both equations can be easily manipulated to cancel out.
2. To cancel out the x variables, we can multiply the first equation by 2 and the second equation by -3. This way, when we add the two equations together, the x variables will cancel out.
3. After completing step 2, the top equation would be:
6x + 8y = 96
4. Line up the two equations and add them together:
(6x + 8y) + (6x + 2y) = 96 + 60
12x + 10y = 156
5. Now we can solve for y by isolating it in the equation:
12x + 10y = 156
10y = 156 - 12x
y = (156 - 12x) / 10
6. Finally, we can solve for x using the value of y obtained in step 5. Substitute the value of y in one of the original equations and solve for x. Let's use the first equation:
3x + 4y = 48
3x + 4((156 - 12x) / 10) = 48
30x + 4(156 - 12x) = 480
30x + 624 - 48x = 480
-18x = -144
x = -144 / -18
x = 8
Therefore, the solution to the system of equations is x = 8 and y = (156 - 12x) / 10.