3x + 4y = 48
6x + 2y = 60
Select the correct option for each question
Choose the best method to solve by looking at the way the equations are set up for you:
Using the best method, how could you get the x variables to cancel out?
After you complete step 2, what would your top equation be?
Line them up and add the equations together to get:
The best method to solve the given system of equations is by elimination.
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 the same coefficient for x in both equations.
2(3x + 4y) = 2(48)
6x + 8y = 96
3(6x + 2y) = 3(60)
18x + 6y = 180
After completing step 2, the top equation would be:
6x + 8y = 96
To solve the system of equations 3x + 4y = 48 and 6x + 2y = 60:
1. From the given equations, it is clear that the x coefficients in both equations are multiples of each other. Thus, we can cancel out the x variables by multiplying the first equation by 2 and the second equation by -3.
New equation (1): 2(3x + 4y) = 2(48) => 6x + 8y = 96
New equation (2): -3(6x + 2y) = -3(60) => -18x - 6y = -180
2. We now have two equations with the x variables cancelled out. To find a solution, we can add the two equations together.
(6x + 8y) + (-18x - 6y) = 96 + (-180)
-12x + 2y = -84
Therefore, after completing step 2, the top equation would be -12x + 2y = -84.
Note: We could also have chosen to multiply the first equation by -2 and the second equation by 3 to cancel out the x variables. The resulting equation and the answer would be the same.
To solve the given system of equations:
Step 1: Examine the equations and determine the best method to solve them. Looking at the coefficients of the x and y terms, it appears that the elimination method would be the most suitable approach.
Step 2: Multiply one or both of the equations by appropriate coefficients to make the coefficients of the x terms equal in magnitude but opposite in sign. In this case, multiplying the first equation by 2 and the second equation by 3 would make the coefficients of the x terms equal:
Equation 1: 6x + 8y = 96
Equation 2: 18x + 6y = 180
Step 3: Line up the equations and add them together to eliminate the x terms:
(6x + 8y) + (18x + 6y) = 96 + 180
Simplifying the left side: 24x + 14y = 276
Therefore, the top equation after completing step 2 would be 24x + 14y = 276.