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### Unit VI Lesson 3

 Systems of Linear Equations (Simultaneous Equations)When you have a system of equations, you will be looking for the one point (the ordered pair, the x and y coordinate on a graph) at which two linear equations are satisfied.  To solve a system of equations, you try to find the values of the unknowns that satisfy both equations in the system.  You can solve by elimination, substitution, or multiplication. Note:  some pairs of equations have no common solution; they might be parallel lines on the graph.One way to solve is by graphing.  Put each equation into the slope-intercept form ( y = mx + b) of a linear equation; then for each equation, you can plot the y-intercept (0,___) from b value and use the slope (m) to get the second point and you have the two points to determine a line. Do likewise for second equation, and the solution is the coordinate of the point where two lines intersect.  Sal at Khan demonstrates and you can practice.You can also solve the systems of equations by manipulating the equations using substitution, elimination, or multiplication with elimination.  Try your hand at a mix of these methods.  You can practice some more at the regents prep site or at the mathiscool site. Now you can do the "mechanics" of solving systems of equations. But on the GED math test, it is very likely that you will find systems of equations in the form of a word problem.  Fortunately, Khan gives us some explanations here and here and then you get a chance to practice on word problems using your skills to set up the system of equations and then solve.  Get some more practice at the Regentsprep website.Lesson 4, patterns and functions ahead.