Question

How do you use substitution to solve the system of equations `3x - 7= y` and `2x + 5y = 16`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Because the first equation is already solved for `y` we can substitute `3x - 7` for `y` in the second equation and solve for `x`:

`2x + 5y = 16` becomes:

`2x + 5(3x - 7) = 16`

`2x + (5 xx 3x) - (5 xx 7) = 16`

`2x + 15x - 35 = 16`

`17x - 35 = 16`

`17x - 35 + color(red)(35) = 16 + color(red)(35)`

`17x - 0 = 51`

`17x = 51`

`(17x)/color(red)(17) = 51/color(red)(17)`

`(color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17)) = 3`

`x = 3`

Step 2) Substitute `3` for `x` in the first equation and calculate `y`:

`3x - 7 = y` becomes:

`(3 xx 3) - 7 = y`

`9 - 7 = y`

`2 = y`

`y = 2`

The solution is: `x = 3` and `y = 2` or `(3, 2)`