Question

How do you solve the system of linear equations `2y+6=x` and `3y+10=x`?

Answer 1

Since x is already isolated in both equations we can easily solve for y by substitution.

Explanation:

`2y + 6 = 3y + 10`

`2y - 3y = 10 - 6`

`-y = 4`

`y = -4`

Now solve for x by substituting -4 for y in either one of the equations.

`2(-4) + 6 = x`

`-8 + 6 = x`

`-2 = x`

The solution set is `{-2, -4}`.

Here are a few of the most fundamental rules for solving systems of equations by substitution.

1. Always solve for the easiest variable in the equation. For example, in `6x + 3y = -9`, it would be easiest to solve for y because you don't end up with fractions, which can become long and tricky to work with.

2. Always only replace the value of x or y in the equation. Don't get rid of any coefficients x or y may have. Example:

If you want to substitute 2x + 3 = y into `4x - 2y = -3`, you must only replace y:

#4x - 2(2x + 3) = -3

You would then distribute and then solve.

Practice exercises:

1. Solve the following linear systems of equations by substitution.

a). `x + 3y = -3, 2x - 2y = 10`

b). `2x + 3y = 10, -3x + 4y = 36`

Good luck!