Use Substitution to solve 2x + y = 35 and 3x + 4y = 65
Christopher Martinez
Published Jan 20, 2026
Use the substitution method to solve:
2x + y = 35
3x + 4y = 65
Check Format
Equation 1 is in the correct format.
Check Format
Equation 2 is in the correct format.
Rearrange Equation 2 to solve for x:
3x + 4y = 65
Subtract 4y from both sides to isolate x:
3x + 4y - 4y = 65 - 4y
3x = 65 - 4y
Now divide by 3:
Revised Equation 2:
| x = | 65 - 4y |
| 3 |
Plug Revised Equation 2 value into x:
2(x) + y = 35
2 * ((65 - 4y)/3) + y = 35
((130 - 8y)/3) + y = 35
Multiply equation 1 through by 3
3 * (((130 - 8y)/3) + y = 35)
3 * (((130 - 8y)/3) + y = 35)
130 - 8y + 3y = 105
Group like terms:
-8y + 3y = 105 - 130
-5y = -25
Divide each side by -5
| y = | -25 |
| -5 |
y = 5
Plug this answer into Equation 1
2x + 1(5) = 35
2x + 5 = 35
2x = 35 - 5
2x = 30
Divide each side by 2
| x = | 30 |
| 2 |
x = 15
What is the Answer?
x = 15 and y = 5
How does the Simultaneous Equations Calculator work?
Free Simultaneous Equations Calculator - Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:
1) Substitution Method (Direct Substitution)
2) Elimination Method
3) Cramers Method or Cramers Rule
Pick any 3 of the methods to solve the systems of equations
2 equations 2 unknowns
This calculator has 2 inputs.
What 1 formula is used for the Simultaneous Equations Calculator?
What 7 concepts are covered in the Simultaneous Equations Calculator?
- cramers rule
- an explicit formula for the solution of a system of linear equations with as many equations as unknowns
- eliminate
- to remove, to get rid of or put an end to
- equation
- a statement declaring two mathematical expressions are equal
- simultaneous equations
- two or more algebraic equations that share variables
- substitute
- to put in the place of another. To replace one value with another
- unknown
- a number or value we do not know
- variable
- Alphabetic character representing a number
