# To solve:the system of equation

To solve:
the system of equation $2x+3y=5\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}6x+9y=15$.

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nitruraviX

Calculation:
Plot
$2x+3y=5$
$0+3y=5$
$y=\frac{5}{3}$
$y=1.1667$
Put $y=0$
$2x+3y=5$
$2x+0=5$
$x=2.5$
Plot the above equations for coordinates (0, 1.667) and (2.5, 0) satisfying the equation.
Plot $6x+9y=15$
Put $x=0$
$6x+9y=15$
$0+9y=15$
$y=\frac{15}{9}$
$y=1.667$
Put $y=0$
$6x+9y=15$
$6x+0=15$
$6x=15$
$x=\frac{15}{6}$
$x=2.5$
Plot the above equation for coordinates (0, 1.667) and (2.5, 0) satisfying the equation.

Since, graph is same for the equations therefore it has infinitely many solutions.
So, the answer is (j), infinite solutions.