How to Solve Simultaneous Linear Congruence Equations

Solving simultaneous linear equations of the form y = ax + b is an important concept in Algebra II that higher level math classes, such as Linear Algebra, build upon. There are many ways to solve these equations, including graphing the equations on the same set of x and y axes to determine where the equations intersect, but a more sophisticated way to go about solving these equations involves manipulating the coefficients in order to subtract one of the equations from the other.

Instructions

1. Locate terms in the system of equations that can potentially be subtracted from each other. If your set of equations is (1) 7x + 8y = 21 and (2) 3x + 4y = 12, notice that you can multiply the second equation by 2, then subtract it from the first equation, to get rid of the y-term entirely.

2. Carry out the operation on which you decided in Step 1. Multiplying (2) by 2 gives 6x + 8y = 24. Subtracting each term in (2) from (1) gives x = -3.

3. Plug this value of x back into either of the original equations, to find the value of y. Plugging into (1) gives -21 + 8y = 21, meaning that 8y = 42 and y = 21/4.

4. Graph your simultaneous equations, and make sure that they do indeed intersect at (-3, 21/4).

References

• The Math Page: Simultaneous Linear Equations