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System of equations

Solving systems of equations

Three methods of solving systems of two linear equations are ilustrated here:

1. Solution by substitution .Find the value of one unknown in either of the given equations and substitute this value in the other equation.

2. Solution by elimination.
If necessary, multiply the given equations by such numbers as will make the coefficients of one unknown in the resulting equation numerically equal. If the signs of the equal coefficients are unlike, add the resulting equations; if like, subtract them.

3. Graphical solution.
Graph both equations, obtaining two straight lines. The simultaneous solution is given by the coordinates (x,y) of the point of intersection of these lines.

Solve the simultaneous equations:

 $\left{10x-y=9\\9x-3y=-15$ x= y=