Question

Solve the following system of linear equations graphically, Also find the points where the lines meet the x−axis or y−axis.

$2x-y=4;3y-x=3,y-axis$

Answer 1

Step 1:Solving and Analyzing the first equation to find the values for $xandy$

considering the first equation given

$2x-y=4.................................\left(1\right)$

Solving the equation

$2x=4+y$

$2x-4=y.........................\left(2\right),$Let this be the equation of y in terms of x

Now, Substituting x values as $0,1,2$ in equation (2) ,we get the following y-values.

$x$	$0$	$1$	$2$
$y$	$-4$	$-2$	$0$

Step 2:Solving and Analyzing the second equation to find the values for $xandy$

Consider the second equation given,

$3y-x=3.......................\left(3\right)$

Solving the equation (2)

$3y=3+x$

$x=3y-3.................................\left(4\right)$,Let this be the equation of x in terms of y.

Now, Substituting y values as $0,1,2$in equation (4),we get the following x-values.

$x$	$-3$	$0$	$3$
$y$	$0$	$1$	$2$

Step 3:Graphical representation.

Plotting the points obtained on the graph, we get the representation of the solution as given below:-

Hence, the point where the lines meet on y-axis are $(0,1),(0,-4)$.