Solving Linear Equations Review

A linear equation is an equation of the first degree, meaning it has no exponents greater than one. It can be written in the form of $$ax + b = 0$$ , where $$a$$ and $$b$$ are constants.

To isolate a variable, you perform inverse operations to both sides of the equation until the variable is alone on one side. For example, in $$6w - y = 2z$$ , you would add $$y$$ to both sides and then divide by 6.

Solving for a variable means finding the value of that variable that makes the equation true. This often involves rearranging the equation to isolate the variable.

The solution is $$x = 1$$ .

To check if a solution is correct, substitute the solution back into the original equation and verify if both sides are equal.

The slope-intercept form is $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

To find the y-intercept, set $$x = 0$$ . The equation becomes $$2y = 18$$ , so $$y = 9$$ .

The first step is to isolate $$y$$ by subtracting $$2x$$ from both sides, resulting in $$2y = 18 - 2x$$ .

A coefficient is a numerical factor that multiplies a variable. For example, in $$3x + 4 = 0$$ , the coefficient of $$x$$ is 3.

Two equations are equivalent if they have the same solution set, meaning they represent the same line on a graph.