How to Find the Intersection of Two Linear Equations

Two linear equations can be plotted on the same graph to find a solution to the system of equations.
••• Jupiterimages/Photos.com/Getty Images

With graphs, complex equations, and the many different shapes that can be involved, it is no wonder that math is one of the most dreaded subjects for many students. Let me guide you through one type of mathematical problem that you are likely to encounter sometime during your high school math career--how to find the intersection of two linear equations.

    Start by knowing that your answer will be in the form of coordinates, meaning that your final answer should be in the form (x, y). This will help you remember that you need to solve not only for an x-value but also for a y-value.

    Designate one equation as Line 1 and the other equation as Line 2 so that if you need to discuss this with a fellow student or a teacher you are able to keep the two linear equations straight.

    Solve each equation so that they are both equations with the y variable on one side of the equation by itself and the x variable on the other side of the equation with all the functions and numbers. For example, the two equations below are in the format that your equations need to be in before you begin. Line 1: y = 3x+6 Line 2: y = -4x+9

    Set the two equations equal to each other. For example, with the two equations from above: 3x+6 = -4x+9

    Solve this new equation for x following the order of operations (parentheses, exponents, multiplication/division, addition/subtraction). For example, with the equation from above: 3x+6 = -4x+9 3x = -4x+3 (subtracting 6 from both sides) 0 = -7x+3 (subtracting 3x from both sides) -7x = -3 (subtracting 3 from both sides) x = 3/7 (divide both sides by -7)

    Plug your value for x into either of the original equations and solve for y. For our equations from before: 3x+6 = y 3(3/7)+6 = y 9/7+6 = y 7 2/7 = y

    Plug your value for x into the other equation to double check your y value. -4x+9 = y -4(3/7)+9 = y -12/7+9 = y 7 2/7 = y

    Put your x and y values into coordinate form for your final answer. So, for our example our final answer would be (3/7, 7 2/7).

Related Articles

How to Solve Slope-Intercept Form
How to Solve for Both X & Y
How to Find Zeros of Linear Functions
How to Calculate Slope Using the TI-83 Plus
How to Find Missing Coordinates With Slope
How to Graph and Find the Solution on a Calculator
How to Solve Double Inequalities
How to Plot Line Segments on Graphing Calculator
Algebra 1 Compared to Algebra 2
How to Find the Y-Intercept of a Circle
How to Solve a Parabola
How to Convert Graphs to Equations
How to Solve Inequalities
How to Convert Diameter to Square Centimeters
Endpoint Math Formula
How to Find the Height of a Rectangular Pyramid
How to Factorise a Quadratic Expression
How to Write the equation of a Linear Function whose...
How to Find Correlation Coefficient & Coefficient of...
How to Graph a Parabola

Dont Go!

We Have More Great Sciencing Articles!