Systems of Equations: GED Math Review
A system of equations contains two or more equations that involve the same variables. Solving the system means finding values that satisfy all the equations. Two common methods are substitution and elimination.
Method 1: Substitution
Consider: y = x + 2 x + y = 10 Because the first equation already tells us that y equals x + 2, substitute that expression into the second equation. x + (x + 2) = 10 Combine like terms: 2x + 2 = 10 Subtract 2: 2x = 8 Divide by 2: x = 4 Now substitute x = 4 into the first equation: y = 4 + 2 y = 6 So the solution is: (4, 6)
Method 2: Elimination
Consider: x + y = 10 x − y = 2 Add the equations: 2x = 12 Therefore: x = 6 Substitute into either original equation: 6 + y = 10 So: y = 4 The solution is: (6, 4)
Check Your Answer
One of the best habits when solving systems is checking the solution in both original equations. If your values do not work in both equations, go back through your calculations.
Watch Your Signs
Negative signs are a common source of mistakes. When subtracting or adding equations, write each step carefully rather than doing several operations mentally.
Practice With Different Forms
Don't practice only equations that are already arranged conveniently. Work with systems where you must rearrange one equation before using substitution or elimination.
Final Takeaway
For GED Math, become comfortable with both substitution and elimination. Work carefully with signs, show your steps, and check your solution in the original equations.
