How do linier equations work?

Each solution is a pair of numbers (x,y) that make the equation true. Solving a linear equation usually means finding the value of y for a given value of x. If the equation is already in the form y = mx + b, with x and y variables and m and b rational numbers, then the equation can be solved in algebraic terms.

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Each solution is a pair of numbers (x,y) that make the equation true. Solving a linear equation usually means finding the value of y for a given value of x. If the equation is already in the form y = mx + b, with x and y variables and m and b rational numbers, then the equation can be solved in algebraic terms.

Step-by-step explanation:

Solving an equation means finding the value or values for which the two expressions on each side of the equals sign are equal. One of the most common methods used to solve equations is the balance method.

Imagine an equation as a set of scales. The scales will stay in balance as long as the same operation (addition, subtraction, multiplication or division) is applied to both sides.

Example: y = 2x + 1 is a linear equation:

line on a graph

The graph of y = 2x+1 is a straight line

When x increases, y increases twice as fast, so we need 2x

When x is 0, y is already 1. So +1 is also needed

And so: y = 2x + 1

Here are some example values:

xy = 2x + 1

-1y = 2 × (-1) + 1 = -1

0y = 2 × 0 + 1 = 1

1y = 2 × 1 + 1 = 3

2y = 2 × 2 + 1 = 5

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step-by-step explanation: