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Now, just what does a solution to a system of two equations represent?Well if you think about it both of the equations in the system are lines. As you can see the solution to the system is the coordinates of the point where the two lines intersect.
\[\begin5\left( \right) 4y & = 1\\ 10y \frac 4y & = 1\\ 14y & = 1 - \frac = - \frac\\ y & = - \left( \right)\left( \right)\\ y & = - \frac\end\] Finally, substitute this into the original substitution to find \(x\).
\[x = 2\left( \right) \frac = - \frac \frac = \frac\] So, the solution to this system is \(x = \frac\) and \(y = - \frac\).
\[3x - 7 = y\] Now, substitute this into the second equation.
\[2x 3\left( \right) = 1\] This is an equation in \(x\) that we can solve so let’s do that.
The first method is called the method of substitution.
In this method we will solve one of the equations for one of the variables and substitute this into the other equation.
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