Question

Estimate the solution to the following system of equations by graphing.

Answer 1

Solution of 9x+8y=26 and 3x+2y=9 are given by $\mathbf{x=\frac{10}{3},y=-\frac{1}{2}}$.

We have to plot the graphs of the given two lines or curves, then we have to find the intersection point(s) of the curves or lines. That point is the solution for the system of the equations.

Given equations are,

$9x+8y=26$ .................(1)

$3x+2y=9$ ...................(2)

Now multiplying 3 with (2) and then subtracting (1) from that we get,

$3(3x+2y)-(9x+8y)=3\times9-26\\\Rightarrow9x+6y-9x-8y=27-26\\\Rightarrow-2y=1\\\Rightarrow y=\frac{-1}{2}$

Substituting the value of y in (1) we get,

$9x+8\times\frac{-1}{2}=26\\\Rightarrow9x-4=26\\\Rightarrow9x=26+4\\\Rightarrow x=\frac{30}{9}=\frac{10}{3}$

Also if we draw the graphs of the given equations by using graphing calculator we get,

Here in the graph we can see that the lines represented by the given equations intersects each other at point $\left(\frac{10}{3},-\frac{1}{2}\right)$.

Hence the solution is $x=\frac{10}{3},y=-\frac{1}{2}$.

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