# Find the solution set of the following using 3 methods.  2x + y = 15; x – y = 9

The given system of equations can be solved using three different methods: graphical, substitution, and elimination.

Solution Using Graphical Method:
To solve the set of linear equations 2x + y = 15 and x – y = 9 graphically, plot both lines on a coordinate plane. From the plot of two lines, identify the point of intersection which is the solution for this equation (2x + y = 15) – (x – y = 9). The coordinates of that point are (6,9) therefore x=6 and y=9. This answer is also confirmed by substituting 6 for x in the second equation to get 6 – 9=-3 which does not equal 0. Thus, we have found our solution set to be {(6,9)} .

## Find the solution set of the following using 3 methods.  2x + y = 15; x – y = 9

Solution Using Substitution Method:
In order to find the solution set using substitution method we need to first isolate either one variable from one equation or another variable from another equation such as in our case; let us choose ‘y’ from 2x+y=15 by subtracting “2x” then solve it for ‘y’ i.e., “y=15-2x” now substitute this value in other equation i.e., “ x- (15-2x)=9 ” solving above gives us our unknown variable as; x=6 & y=(15-12)=3 thus making our final solution set as {(6 , 3 )}.

Solution Using Elimination Method:
To solve these equations using elimination method first add both equations together so that one of them gets cancelled out leaving only one variable in single equation like here we would get ; 3x +0y = 24 after re arranging it further we will get ; 3X =24/3 thus X=8 now plugging back X value into any original equation say 2X+Y=”15″ will give us “Y” value as 7 making our Solution Set as {(8 ,7)} .

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