solve the following system of linear equations graphically
x+y=10 ; x+y=4
Answers
Step-by-step explanation:
For x + y = 10, it can be written as y = 10 - x
xy=10−x100010
For equation x - y = 4, it can be written as y = x - 4
xy=x−4400−4
Now we plot the points A (10, 0), B(0, 10) and P(4, 0), Q(0, 4) on the graph paper.
We observe that the two lines representing the two equations are intersecting at the point (7, 3). Hence, x=7y=3} is a solution of given equations.
EXPLANATION.
Graphical equation.
⇒ x + y = 10. - - - - - (1).
⇒ x + y = 4. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ x + y = 10. - - - - - (1).
Put the value of x = 0 in equation, we get.
⇒ (0) + y = 10.
⇒ y = 10.
Their Co-ordinates = (0,10).
Put the value of y = 0 in equation, we get.
⇒ x + (0) = 10.
⇒ x = 10.
Their Co-ordinates = (10,0).
From equation (2), we get.
⇒ x + y = 4. - - - - - (2).
Put the value of x = 0 in equation, we get.
⇒ (0) + y = 4.
⇒ y = 4.
Their Co-ordinates = (0,4).
Put the value of y = 0 in equation, we get.
⇒ x + (0) = 4.
⇒ x = 4.
Their Co-ordinates = (4,0).
Both equation never intersects each other & are parallel to each other.
