Solving by Substitution
Grade 8 · Math · Systems of Equations · Nebraska, USA
Lesson Summary
Solve a system by replacing one variable with an expression from the other equation.
Explanation
In the substitution method, you solve one equation for one variable, then plug that expression into the other equation. This gives you a single equation with one variable, which you can solve normally. Once you find that variable, substitute back to find the other one. This method works best when one equation already has a variable isolated, like y = 3x + 2.
Practice Questions
Q1: Solve: y = 2x and x + y = 9.
Answer: Substitute y = 2x into x + y = 9 to get x + 2x = 9, so 3x = 9 and x = 3. Then y = 2(3) = 6. Solution: (3, 6).
Q2: Solve: y = x − 1 and 2x + y = 8.
Answer: Substitute y = x − 1 into 2x + y = 8: 2x + (x − 1) = 8, so 3x − 1 = 8, 3x = 9, x = 3, y = 2. Solution: (3, 2).
Q3: When is substitution the easiest method to use?
Answer: When one equation is already solved for a single variable, so you can plug it directly into the other equation.
People Also Ask
What is Solving by Substitution in Grade 8 Math?+
Solving by Substitution is a lesson in the Systems of Equations chapter of Grade 8 Math. It is part of the Nebraska, USA school curriculum and covers key concepts that students need to understand at this level.
What grade level covers Solving by Substitution?+
Solving by Substitution is taught in Grade 8 as part of the Math curriculum in Nebraska, USA.
How can I help my child with Systems of Equations in Math?+
Start with the lesson summary and explanation on this page. Practice the questions provided, then use TutorTom for personalized, step-by-step help with Systems of Equations topics.