Question

To solve this system, you could do the following steps:

3x+4y=48

6x+2y=60
Choose the best method to solve by looking at the way the equations are set up for you

Answer 1

The best method to solve this system of equations is by using the method of substitution.

1. Start by solving one of the equations for one variable in terms of the other variable. Let's solve the first equation for x:
3x + 4y = 48
3x = 48 - 4y
x = (48 - 4y) / 3

2. Substitute the expression for x in terms of y into the other equation. Let's substitute in the second equation:
6x + 2y = 60
6((48 - 4y) / 3) + 2y = 60

3. Simplify and solve for y:
16 - 8y + 2y = 60
-6y + 16 = 60
-6y = 60 - 16
-6y = 44
y = 44 / -6
y = -22/3 or approximately -7.333

4. Substitute the value of y back into the expression for x to find the corresponding value:
x = (48 - 4(-22/3)) / 3
x = (48 + 88/3) / 3
x = (144/3 + 88/3) / 3
x = (232/3) / 3
x = 232/9 or approximately 25.778

5. So the solution to the system of equations is x = 232/9 and y = -22/3.