solve each of the following systems of linaer quation graphically. the check if the system of linaer aquations has no solution.
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>>Solve the following system of linear equ
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Solve the following system of linear equations graphically. Also, find the coordinates of the points where the lines meet the y − axis.
2x−y−5=0
x−y−3=0
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Given lines: 2x−y−5=0 and x−y−3=0
The line 2x−y−5=0 can be written as y=2x−5 ...(1)
x 0 1 3
y -5 -3 1
The line x−y−3=0 can be written as x=3+y ...(2)
x 0 3 4
y -3 0 1
Let us substitute x=3+y in equation (1)
⇒2(3+y)−y−5=0
⇒6+2y−y−5=0
⇒y=−1
∴ x=2
∴ The lines meet at the point (2,−1)
The coordinates where the lines meet y − axis are (0,−3) and (0,−5).