Solve graphically each of the following systems of linear equations. Also find the coordinates of the points where the lines meet axis of y.
Solve graphically each of the following systems of linear equations. Also find the coordinates of the points where the lines meet axis of y.
(i) $2 x-5 y+4=0$
$2 x+y-8=0$
(ii) $3 x+2 y=12$
$5 x-2 y=4$
(iii) $2 x+y-11=0$,
$x-y-1=0$
(iv) $x+2 y-7=0$
$2 x-y-4=0$
(v) $3 x+y-5=0$
$2 x-y-5=0$
(vi) $2 x-y-5=0$,
$x-y-3=0$
(i) The given equations are
$2 x-5 y+4=0$...(i)
$2 x+y-8=0$ ..(ii)
The two points satisfying (i) can be listed in a table as,
The two points satisfying (ii) can be listed in a table as,
Now, graph of equations (i) and (ii) can be drawn as,
It is seen that the solution of the given system of equations is given by x = 3, y = 2.
Also, it is observed that the lines (i) and (ii) meet the $y$-axis at the points $\left(0, \frac{4}{5}\right)$ and $(0,8)$ respectively.
(ii) The given equations are
$3 x+2 y=12$....(i)
$5 x-2 y=4$...(ii)
The two points satisfying (i) can be listed in a table as,
It is seen that the solution of the given system of equations is given by x = 2, y = 3.
Also, it is observed that the lines (i) and (ii) meet the $y$-axis at the points $(0,6)$ and $(0,-2)$ respectively.
(iii) The given equations are
$2 x+y-11=0$..(i)
$x-y-1=0$..(ii)
The two points satisfying (i) can be listed in a table as,
It is seen that the solution of the given system of equations is given by x = 4, y = 3.
Also, it is observed that the lines (i) and (ii) meet the $y$-axis at the points $(0,11)$ and $(0,-1)$ respectively.
(iv) The given equations are
$x+2 y-7=0$...(i)
$2 x-y-4=0$....(ii)
The two points satisfying (i) can be listed in a table as,
It is seen that the solution of the given system of equations is given by x = 3, y = 2.
Also, it is observed that the lines (i) and (ii) meet the $v$-axis at the points $(0,3.5)$ and $(0,-4)$ respectivelv.(v) The given equations are
$3 x+y-5=0$...(i)
$2 x-y-5=0$....(ii)
The two points satisfying (i) can be listed in a table as,
It is seen that the solution of the given system of equations is given by x = 2, y = −1.
Also, it is observed that the lines (i) and (ii) meet the $y$-axis at the points $(0,5)$ and $(0,-5)$ respectively.
(vi) The given equations are
$2 x-y-5=0$..(i)
$x-y-3=0$..(ii)
The two points satisfying (i) can be listed in a table as,
It is seen that the solution of the given system of equations is given by x = 2, y = −1.
Also, it is observed that the lines (i) and (ii) meet the $y$-axis at the points $(0,-3)$ and $(0,-5)$ respectively.