If y = 2x + 1, then anywhere a y appears you may write 2x + 1 instead.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Why this helps
The second equation then contains only x, and one equation with one letter can be solved.
Finish the job
Having found x, put it back into either equation to get y. A system needs both numbers.
Check in both
The pair must satisfy both equations, not just the one you solved.
Replace one letter
Rearrange one equation to express one variable in terms of the other, then substitute that expression into the second equation. You are left with one equation in one variable, which you already know how to solve.
Choose the easiest rearrangement
If one equation already has a variable alone — y = 3x + 1 — substitute that. Otherwise pick the variable with a coefficient of 1 to avoid fractions. The method works either way, but one choice is much less painful.
Substitute back to find the other
Solving gives one value; put it back into either original equation to find the other. Using the simpler equation for this is quicker, and using the other one afterwards is a free check.
Use brackets when substituting
Replacing y with 3x + 1 in 2y = 10 gives 2(3x + 1) = 10, not 2 × 3x + 1. Bracketing the substituted expression prevents the commonest error in the method by making the multiplication apply to all of it.
Step 2: Try It Yourself
Tap and try it out.
The slope is 2: for every 1 across, the line goes 2 up.
Step 3: Watch an Example
One step at a time.
Watch Ana Substitute
y = 2x + 1 and 3x + y = 11.
- Step 1
The first equation already gives y on its own.
Step 4: Your Turn
Practice makes it stick.
The Substitution
Problem 1 of 2
y = 3x and x + y = 12. What is x?
The Other Half
Problem 2 of 2
Same system. What is y?
Swap It In
1 of 4
y = x + 2 and x + y = 10. What is x?
2 of 4
Same system. What is y?
3 of 4
y = 2x and 3x + y = 20. What is x?
4 of 4
Does a solution have to satisfy both equations? 1 for yes, 0 for no.
Step 5: Quick Check
Show what you know.
Question 1 of 1
y = 4x and x + y = 15. What is x?
What You Learned
- Substitution replaces one letter with an expression in the other.
- That leaves one equation in one unknown, which can be solved.
- Put the answer back to find the second value, then check both equations.