solve graphically the pair of equations : 3x+y-3=0 , 2x-y+8=0 . Write the coordinates of the vertices of the triangle formed by two lines with x-axis.
Answers
Given, pair of linear equation
4x−5y=20
5y=4x−20
y=
5
4x−20
Putting x=0,
y=
5
4×0−20
=
5
−20
y=−4
Putting x=2,y=
5
4×2−20
=
5
8−20
y=
5
−12
y=−2.4
Putting x=5,y=
5
4×5−20
=
5
20−20
y=0
Table : 1
x=0,2,5
y=−4,−2.4,0
From equation (ii),.
3x+5y=15
5y=15−3x
y=
5
15−3x
Putting x=0,y=
5
15−3×0
=
5
15−0
y=3
Putting x=5,y=
5
15−3×(5)
=
5
15−15
y=0
Putting x=−5,y=
5
15−3×(−5)
=
5
15+15
=6
Table : 2
x=0,5,−5
y=3,0,6
Plot the points obtained from Table (1) and (2) on graph paper. By joining these points two straight lines are obtained.
From the given graph it is clear that two lines intersect each other at point P(5,0)
∴x=5 and y=0 are required solution.
(0,3),(0,−4) and (5,0) are co-ordinates of vertices of ΔABP formed by two straight lines at y-axis.
Answer:
+3y+5=0....(1)
3x−2y−12=0......(2)
Isolate x from equation (1) and find the value of x and y.
2x+3y+5=0
2x=−3y−5
x=(−3y−5)/2
x: −4 −1 2
y: 1 −1 −3
Similarly, isolate x from equation (2) and find the values of x and y.
3x−2y−12=0
or 3x=2y+12
or x=(2y+12)/3
x: 4 0 2
y: 0 −6 −3
Graph:
Both the lines intersect each other at point (2,−3).
So, x=2,y=−3