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Question
Solve the following pair of equations graphically.
2x−3y−6=0;2x+y+10=0
2x−3y−6=0;2x+y+10=0
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Solution
From equation
2x−3y−6=0
⇒2x=3y+6
⇒x=3y+62 ........(i)
when y=0,x=3×0+62=3
when y=−1,x=3×(−1)+62=32=1.5
when y=−2,x=3×(−2)+62=−6+62=0
Table for equation (i)
x=3,1.5,0y=0,−1,−2
Similarly from equation 2x+y+10=0
⇒y=−2x−10
when x=−2,y=−2×−2−10
=4−10=−6
when x=−3,y=−2×−3−10
=6−10=−4
when x=−4,y=−2×−4−10
=8−10=−2
Table for equation (ii)
x=−2,−3,−4y=−6,−4,−2
Now plotting and joining the points from table (i) and (ii) we find that the lines are intersecting at a point (−3,−4).
Hence, the required solution is (−3,−4).
2x−3y−6=0
⇒2x=3y+6
⇒x=3y+62 ........(i)
when y=0,x=3×0+62=3
when y=−1,x=3×(−1)+62=32=1.5
when y=−2,x=3×(−2)+62=−6+62=0
Table for equation (i)
x=3,1.5,0
y=0,−1,−2
Similarly from equation 2x+y+10=0
⇒y=−2x−10
when x=−2,y=−2×−2−10
=4−10=−6
when x=−3,y=−2×−3−10
=6−10=−4
when x=−4,y=−2×−4−10
=8−10=−2
Table for equation (ii)
x=−2,−3,−4
Similarly from equation 2x+y+10=0
⇒y=−2x−10
when x=−2,y=−2×−2−10
=4−10=−6
when x=−3,y=−2×−3−10
=6−10=−4
when x=−4,y=−2×−4−10
=8−10=−2
Table for equation (ii)
x=−2,−3,−4
y=−6,−4,−2
Now plotting and joining the points from table (i) and (ii) we find that the lines are intersecting at a point (−3,−4).
Hence, the required solution is (−3,−4).
Now plotting and joining the points from table (i) and (ii) we find that the lines are intersecting at a point (−3,−4).
Hence, the required solution is (−3,−4).
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