Linear equations (two variables)

A linear equation in two variables is an equation that can be written in the form $$ax + by = c$$ , where $$a$$ , $$b$$ , and $$c$$ are constants, and $$x$$ and $$y$$ are variables.

The graph of a linear equation represents all the solutions of the equation, plotted as a straight line on the coordinate plane.

The slope of a line in the equation form $$y = mx + b$$ is given by $$m$$ , which represents the change in $$y$$ for a unit change in $$x$$ .

The y-intercept is the point where the line crosses the y-axis, represented by the value of $$b$$ in the equation $$y = mx + b$$ .

To solve a system of linear equations by graphing, plot both equations on the same coordinate plane and identify the point where the two lines intersect.

If two lines are parallel, it means they have the same slope and will never intersect, indicating that there is no solution to the system.

If two lines are coincident, it means they lie on top of each other, indicating that there are infinitely many solutions to the system.

The solution of a system of equations can be determined graphically by finding the coordinates of the intersection point of the two lines.

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.