1.

Solvegraphically the system of linear equations4x - 5y+16=0 and2x+y - 6 = 0 .Determinethe verticesof the vertices of the triangle formedby theselinesand thex-axis.

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Solution :On a graph PAPER, draw horizontlline `X'OX ` and verticalline `YOY'`as the x - axisand the y - axis respectively.
Graphof `4x-5y+ 16 = 0 `
`4 x-5y+16 = 0 rArr5y=4x+16`
` ""rArry =((4x +16))/( 5)""` ... (i)
Putting` x = - 4 ` in (i), we get`y = 0 `
Putting` x =1 ` in(i), we get`y =4`
Putting` x =6` in (i), we get `y = 8`
Thus, we havethe followingtable for` 4x -5y+ 16 = 0`

Now,plotthe points` A(-4, 0), B(1, 4)andC(6, 8)` on the graph paper.
JoinAB and BC to get thegraphline ABC. Extendit onboth ways.
Thus,the line ABC is the graph of `4x - 5y + 16 = 0`
Graphof `2x+ y-6 = 0`
` 2x + y - 6 = 0 rArry =( 6 -2x )""`... (ii)
Putting` x = 0 ` in(ii),we get` y =6 `.
Putting ` x =2 `in (ii), we get` y =2 `
Putting ` x =3 `in(ii), we get`y = 0 `
Thus, we havethe followingtable for `2x+ y -6 = 0`

On the samegraphpaper as above, plot the points
`P(0, 6), Q(2, 2 ) and R(3, 0)`
Join PQand QR to get the graph line PQR. Extendit onboth ways.
Thus, theline PQR is the graphof ` 2x + y - 6 = 0`

The two graphslines ABC and PQR intesectat the point ` B (1, 4 )`.
` thereforex= 1AND y =4` is thesolution of the givensystem ofequations.
These lines from`Delta BAR` withthe x -axis , whose verticesare ` B(1, 4), A(-4, 0) and R(3, 0)`


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