Determine, graphically whether the system of equations x – 2y = 2, 4x – 2y = 5 is consistent or in-consistent.
Answers
Equations are consistent x – 2y = 2, 4x – 2y = 5
Step-by-step explanation:
x x - 2y = 2 4x - 2y = 5
x y y
-4 -3 -10.5
-3 -2.5 -8.5
-2 -2 -6.5
-1 -1.5 -4.5
0 -1 -2.5
1 -0.5 -0.5
2 0 1.5
3 0.5 3.5
4 1 5.5
Both equation intersect at (1 , -0.5)
hence Equations are consistent
equations is called as consistent if there is at least one set of values for the unknowns that satisfies each equation in the system
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Answer:
Step-by-step explanation:
x – 2y = 2……. (i)
4x – 2y = 5……. (ii)
For equation (i),
⇒ y = (x – 2)/2
When x = 2, we have y = (2 – 2)/2 = 0
When x = 0, we have y = (0 – 2)/2 = -1
For equation (ii),
We solve for x:
⇒ x = (5 + 2y)/4
So, when y = 0
x = (5 + 2(0))/4 = 5/4
And, when y = 1.5
⇒ x = (5 + 2(1))/4 = 7/4
Graph of the equations (i) and (ii) is as below:
It is clearly seen that the two lines intersect at (1,0)
Hence, the system of equations is consistent.
