Solving Systems of Equations by Graphing – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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A system of equation is two or more equations with the same variables. To determine the point where the equations meet, the solution to the system, there are several methods: graphing, substitution, and elimination.

This video investigates how to use graphs to solve systems of equations. To determine where lines will meet on the coordinate plane (coordinate grid), manipulate each equation in the system, so it is written in slope-intercept form, y = mx + b. You can do this by isolating the y-value or the vertical coordinate.

Now using information from the equations written in slope-intercept form, you can graph the lines. Remember b is the y-intercept, and m is the slope or the rise over the run. First, mark the y-intercept, then using the slope value, you can mark a couple other points on the line and last connect the dots to draw a line. Do this for every equation in the system. The point where the lines intersect is the solution to the system and also the ordered pair that will satisfy all the equations in the solution.

How can a system of equations be useful in the real world? Well imagine you want to accidentally bump into someone, if you knew the equation of their path and the equation of your path… To learn more about this topic, watch the video.

Solve systems of equations to find solutions to problems.



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Exercises in this Practice Problem
Describe how to graph $y=\frac12x+2$.
Use a graph to show the paths of Red Riding Hood and the Wolf.
Determine whether or not Red Riding Hood and her grandmother meet.
Decide if the lines have a point of intersection.
Describe how to change $2y-4=x$ into slope-intercept form.
Analyze whether or not the lines have a point of intersection with the line of $y=-\frac13x+2$