Check out whether the graph according to the question is correct. (If wrong then kindly solve the problem)
Que. solve graphically
the system of
linear equations
4x-5y +16=0 and 2x+y-16=0
Determine the vertices of the triangle formed by these lines and the x-axis.
Answers
QUESTIONS
Draw the graph of the equations 4x – 5y + 16 = 0 and 2x + y – 6 = 0. Determine the vertices of the triangle formed by these lines and the x-axis.
SOLUTION:-
Graph of 4x-5y+16=0
=>5y=4x+16
=>y=(4x+16)/5......(1)
Putting x=-4 in (1) we get :y=0
Putting x=1 in (1) we get :y=4
Putting x =6 in (1) we get :y=8
Thus we have the following table for 4x-5y+16=0
_________
x | 4 | 1 | 6 |
y | 0 | 4 | 8 |
Graph of 2x+y-6=0
=>y=(6-2x)........(2)
Putting x =0 in (2) we get : y=6
Putting x=2 in (2) we get :y=2
Putting x=3 in (2) we get :y=0
Thus we have the following table for 2x+y-6=0
_________
x | 0 | 2 | 3 |
y | 6 | 2 | 0 |
In the above figure by plotting these points we get the solution of this equation on which the two lines intersect i.e B(1,4)
Therefore x=1 ,y=4 is the solution of the given system of equation
These lines form triangle BAR with x-axis ,whose vertices are B(1,4),A(-4,0) and R(3,0)
