Question

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

$\left(ix\right)2x-5y+4=0;2x+y-8=0,y-axis$

Answer 1

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

consider the first equation given

$2x-5y+4=0...............................\left(1\right)$

Solving the equation

$2x=5y-4$

$x=\frac{5y-4}{2}............................\left(2\right)$,Let this be the equation of x in terms of y

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

$x$	$-2$	$0.5$	$3$
$y$	$0$	$1$	$2$

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

Consider the second equation given,

$2x+y-8=0...........................\left(3\right)$

Solving the equation

$y=8-2x...........................\left(4\right)$,Let this be the equation of y in terms of x.

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

$x$	$0$	$1$	$2$
$y$	$8$	$6$	$4$

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 $(0,8),(0,0.8)$.