What you’ll learn
Solve systems by substitution.
Key idea
Keep its constant when combining like terms; a solution must satisfy both equations.
Dropping the substituted constant changes the intersection; both original equations must hold.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve by substitution: y=-4x-4; x+y=-10. Enter ordered pair (x,y).
- Substitute the entire expression for y: x+(-4x-4)=-10.
- Combine to -3x-4=-10; x=2, then y=-12. Both original constraints hold at (2,-12).
Answer: (2,-12)
Quick Check
Evaluate a worked attempt at solve systems by substitution, identify the first invalid step, and provide the correction.
Solve y=-4x-1; x+y=11. Step 1 substitutes x+(-4x-1)=11. Step 2 drops the constant and writes -3x=11, giving x=-11/3. Identify first invalid step and correct the pair.