Question

How do you solve `35x - 5y = 20` and `y = 7x + 4` using substitution?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for `y` we can substitute `(7x + 4)` for `y` in the first equation and solve for `x`:

`35x - 5y = 20` becomes:

`35x - 5(7x + 4) = 20`

`35x - (5 * 7x) - (5 * 4) = 20`

`35x - 35x - 20 = 20`

`35x - 35x - 20 = 20`

`0 - 20 = 20`

`-20 != 20`

This indicates there are no solutions to this system of equations. Or, no solution set is the empty or null set: `{O/}`

This also indicates, if there is no solutions, that these equations represent parallel lines.

Answer 2

"Substitute" the expression for y in the second equation into the first one.

Explanation:

`35x − 5(7x + 4) = 20`
`35x − 35x - 20 = 20`
`0 = 40`
0 does not = 40, so there is no solution to this set.

Converting both to slope-intercept form gives us:
`35x − 5y = 20` ; `-5y = -35x + 20` Dividing by -5 we get:
`y = 7x - 4`; compared to the second equation
`y = 7x + 4`

They are parallel lines (same slope) with different intercepts (4 and -4).