Question

A system of equations is shown. What is the solution to the system? 4c+2d=11 (7/2)d=41-22c

Answer 1

`c=29/20`
`d=13/5`

Explanation:

I'll start with `4c+2d=11`. Because `d` looks easier in `(7/2)*d=41-22c`, I'll solve for `d`.
`4c+2d=11` Isolate `d` and coefficients on one side:
`2d=11-4c` Isolate `d`:
`d=(11/2)-2c`

Now that we have `d` in terms of `c` we can input it into the other equation:
`(7/2)*((11/2)-2c)=41-22c` Distribute:
`(77/4)-7c=41-22c` Isolate `c` and coefficients on one side:
`15c=87/4` Isolate `c`:
`c=29/20`

We can input this into the first equation to find `d`:
`4(29/20)+2d=11` Combine like terms:
`29/5+2d=11` Isolate `d` and its coefficients on one side:
`2d=26/5`
`d=13/5`