1. Choose the best method to solve by looking at the way the equations are set up for you:
The best method to solve this system of equations is the method of elimination.
2. Using the best method, how could you get the x variables to cancel out?
To cancel out the x variables, you can multiply the first equation by 2 and the second equation by 3. This will make the coefficients of x in both equations equal.
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 = 96 (from step 3)
+ 6x + 2y = 60
Adding the equations together, we get:
12x + 10y = 156
5. Solve for y.
To solve for y, we need to isolate y on one side of the equation. Subtracting 12x from both sides, we get:
10y = 156 - 12x
Dividing both sides by 10, we get:
y = (156 - 12x) / 10
6. Solve for x.
To solve for x, we can substitute the value of y from step 5 into any of the original equations. Let's substitute it into the second equation:
6x + 2((156 - 12x) / 10) = 60
Simplifying the equation, we get:
6x + (312 - 24x) / 10 = 60
Multiplying both sides by 10 to eliminate the fraction, we get:
60x + 312 - 24x = 600
Combining like terms, we get:
36x + 312 = 600
Subtracting 312 from both sides, we get:
36x = 288
Dividing both sides by 36, we get:
x = 8
So the solution to the system of equations is x = 8 and y = (156 - 12(8)) / 10, which simplifies to y = 3.