Definition: To solve a system of equations with three or more variables, the same methods as solving a system of equations with two variables will be helpful. We can still use substitution and elimination (see: Solving Systems of Linear Equations).
Solve for x, y, and z:
Step 1: Using the elimination method, add the first two equations to cancel out the z:
Step 2: Multiply the top equation by 2. This will allow us to eliminate the z when adding the top and bottom equations:
Step 3: Working with this newest equation, divide both sides by 7, then isolate the x:
Step 4: Now that we know x = (7 – y), substitute this into the equation found in Step 1 and simplify to solve for y:
Step 5: Substitute y = 5 into the equation found in Step 3 to solve for x:
Step 6: Plug x = 2 and y = 5 into any of the 3 equations to solve for z:
Our answer will be x = 2, y = 5, z = 4.
Still need help solving systems of equations with 3+ variables? Download Yup and get help from an expert math tutor 24/7