Substitution works when one equation hands you an expression for a variable. You replace that variable in the other equation, which leaves one equation in one unknown.
DeltaMath usually presents one equation as y = … or x = …, which signals substitution is intended. If neither equation is solved for a variable, pick the one with a coefficient of 1 or −1 and rearrange it first.
How to solve it, step by step
Pick the equation already solved for a variable
In the system y = 2x − 1 and 3x + y = 14, the first equation gives y directly.
Substitute into the other equation
Replace y in the second equation with (2x − 1): 3x + (2x − 1) = 14. Keep the parentheses.
Solve the one-variable equation
5x − 1 = 14 → 5x = 15 → x = 3.
Back-substitute to find the other variable
y = 2(3) − 1 = 5.
Check in both equations and write an ordered pair
3(3) + 5 = 14 ✓ and 5 = 2(3) − 1 ✓. Answer: (3, 5).
Worked example
Example 1
Solve the system: x = 4 − 2y and 3x − y = 5.
- Substitute x: 3(4 − 2y) − y = 5
- 12 − 6y − y = 5
- 12 − 7y = 5
- −7y = −7 → y = 1
- x = 4 − 2(1) = 2
- Check: 3(2) − 1 = 5 ✓
Answer (2, 1)
Mistakes DeltaMath marks wrong
- Forgetting to distribute the coefficient to every term inside the parentheses: 3(4 − 2y) is 12 − 6y, not 12 − 2y.
- Substituting back into the same equation you just used, which always "checks" and hides errors.
- Writing the answer as (y, x) instead of (x, y).
- Stopping after finding one variable.
How to type the answer
- Enter the solution as an ordered pair with parentheses and a comma: (3, 5).
- If the variables cancel and you get a true statement (0 = 0), select "infinitely many solutions"; if false (0 = 7), select "no solution".