# How To: Solve a linear system by elimination method

This video is about using the elimination method to solve a linear system. The lady presenting this video says that elimination method means that one of the two variables has to be eliminated while adding up the two linear equations. She then explains the example equations 6x-2y=66 and 5y=-29-2x. She asks you to first line up x and y. So the second equation is rewritten as 2x+5y=-29. Then she says that, to eliminate a variable, we should have their variables equal in value but of opposite signs. Hence she says that the easiest thing to do in this example is to multiply the second equation by -3 so that 2x becomes -6x. So the second equation can be rewritten as -6x-15y=87. When you add up the first equation and the new equation, 6x and -6x get canceled and hence the variable 'x' will be eliminated in the new equation that results from this addition. The new equation you get is -17y=153 which means that the value of y is -9. Next she asks you to substitute y=-9 in the first equation and the result you get is value of x=8. She says that (8,-9) is the point where the two lines intersect. Now to check if this solution is correct, you can substitute x and y values in one of the given equations and see if the equation is true. You can also double check it using the second equation. Next, she takes the example equations 3x-7y=21 and -5x+4y=-35. Here, to eliminate a variable in the same way as before, she multiplies the first equation by 5 and the second equation by 3. The resultant equations are 15x-35y=105 and -15x+12y=-105. When you add up these two equations, you have 'x' eliminated and get the result y=0. By substituting this value in the first equation, you get the result x=7. She says that the point (7,0) is where the two given lines intersect. She also says that you can verify the answer by checking if the given equations are true when this solution is applied on them. Also another way of checking is to make a graph and see if the two lines cross at (7,0).

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