2D Linear Equation Calculator: Solve Two-Variable Systems
What is a 2D Linear Equation Calculator?
A 2D Linear Equation Calculator is like a smart helper that solves puzzles with two clues! It finds the values of two unknown numbers (usually called x and y) that make two math sentences true at the same time. It's like finding the perfect spot where two paths cross!
How to Calculate Two-Variable Systems
To solve a two-variable system, we look at two equations together. We find the values of x and y that work for both equations. It's like finding a treasure using two different maps - the spot where both maps point is our answer!
Formula
A system of two linear equations looks like this:
\[ a_1x + b_1y = c_1 \]
\[ a_2x + b_2y = c_2 \]
Here's what these letters mean:
\(x\) and \(y\) are the unknown numbers we're trying to find
\(a_1\), \(b_1\), and \(c_1\) are numbers in the first equation
\(a_2\), \(b_2\), and \(c_2\) are numbers in the second equation
Calculation Steps
Write down both equations
Use the substitution method or elimination method to solve
Find the value of one variable (like x)
Use that value to find the other variable (y)
Check if the values work in both equations
Example and Visual Representation
Let's solve this system:
\[ 2x + y = 5 \]
\[ x - y = 1 \]
Our calculator finds that x = 2 and y = 1
Let's show this on a graph:
Equation 1: 2x + y = 5Equation 2: x - y = 1Solution: (2, 1)
Solution Steps:
Add the equations to eliminate y:
(2x + y = 5) + (x - y = 1)
→ 3x = 6
→ x = 2
Substitute x = 2 in first equation:
2(2) + y = 5
4 + y = 5
y = 1
Therefore, solution is (2, 1)
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