How do you solve the system of linear equations #2y+6=x# and #3y+10=x#?
Since x is already isolated in both equations we can easily solve for y by substitution.
Now solve for x by substituting -4 for y in either one of the equations.
The solution set is
Here are a few of the most fundamental rules for solving systems of equations by substitution.
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.
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 - 2(2x + 3) = -3
You would then distribute and then solve.
- Solve the following linear systems of equations by substitution.