Solve the following linear equations graphically
3x+5y =4
x-5y =8
Answers
Concept:
We have to first plot the graphs of the given equation using ab graphing calculator then the solution is the intersection point(s) between the curves formed by the equations.
Given:
The given system of linear equations are
3x + 5y = 4
x - 5y = 8
Find:
The solution of the above system of linear equations using graph.
Solution:
The first equation is,
3x+5y = 4
5y = 4-3x
y = (4-3x)/5
When x=3, y = (4-3*3)/5 = -5/5 = -1
When x=8, y = (4-3*8)/5 = -20/5 = -4
When x=-2, y = (4-3*(-2))/5 = 10/5 = 2
So, (3,-1), (8,-4), (-2,2) is satisfied line formed by the equation 3x+5y=4.
Second equation is,
x-5y = 8
x = 8+5y
So when y=-1, x = 8+5(-1) = 8-5 = 3
When y=0, x= 8+5*0 = 8
When y=1, x = 8+5*1 = 8+5 = 13
So (3,-1), (8,0) and (13,1) are satisfied by the line by the equation x-5y = 8.
From the plotted graph we can see that two lines represents the given two equations intersects at (3,-1).
So the solution is x=3 and y=-1.
Hence the solution of the system of linear equations 3x+5y=4 and x-5y=8 is given by x=3 and y=-1.
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Concept
Two linear equations can be solved graphically by finding their point of intersection.
Given
two equations
3x + 5y = 4
x - 5y = 8
Find
we are told to solve the given linear equations graphically
Solution
In 3x + 5y = 4,
if x = 0, y = 4/5
and if y = 0, x = 4/3
Thus, we have two points (0,4/5) and (4/3,0)
Similarly, in x - 5y = 8
if x = 0, y -8/5
and if y = 0, x = 8
Thus, we get two points (0,-8/5) and (8,0)
Now, we plot these two points as shown in the graph below
From the graph we see that the point of intersection of the two lines is (3,-1).
Thus, (3,-1) is the solution.
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