Mathematics

Understanding the Equation 2x + y = 6

An intuitive look at linear equations with two variables, showing how a single equation with two unknowns represents an entire line of possible solutions.

2x + y = 6

What does it actually mean to have two unknown quantities linked by a single rule? Imagine a balance scale where two units of 'x' plus one 'y' must always add up to exactly six.

Step-by-step solver

(Solution) Isolation

Start with the given equation and isolate y by moving the 2x term.

2x + y = 6 \implies y = 6 - 2x

(Solution) Finding Points

Substitute different values of x into the equation to find corresponding y values.

x=0 \implies y=6; \quad x=1 \implies y=4; \quad x=3 \implies y=0

Original question

Solve 2x + y = 6

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