6. Solve the following system of linear equations graphically.
2x + y = 10; 4x - y = 8
Does the point (1, - 4) lie on any one of the lines ? Write the equation.
Answers
Answer:
2x+y=10,4x-y=8
8x+4y=40-(1) 2x+y=10 multiply by 2 and
8x-2y=16(2)4x-y=16 multiply by 4
substructing equation (1) and (2)
(8x+4y)-(8x-2y)=40-16
8x+4y-8x+2y=24
4y+2y=24
6y=24
y=24/6
y=4 answer
EXPLANATION.
Graph of the linear equation.
⇒ 2x + y = 10. - - - - - (1).
⇒ 4x - y = 8. - - - - - (2).
As we know that,
From equation (1), we get.
⇒ 2x + y = 10. - - - - - (1).
Put the value of x = 0 in equation, we get.
⇒ 2(0) + y = 10.
⇒ y = 10.
Their Co-ordinates = (0,10).
Put the value of y = 0 in equation, we get.
⇒ 2x + (0) = 10.
⇒ 2x = 10.
⇒ x = 5.
Their Co-ordinates = (5,0).
From equation (2), we get.
⇒ 4x - y = 8. - - - - - (2).
Put the value of x = 0 in equation, we get.
⇒ 4(0) - y = 8.
⇒ - y = 8.
⇒ y = - 8.
Their Co-ordinates = (0,-8).
Put the value of y = 0 in equation, we get.
⇒ 4x - (0) = 8.
⇒ 4x = 8.
⇒ x = 2.
Their Co-ordinates = (2,0).
Both curves intersects at a point = (3,4).
Yes, the point (1,-4) lie on the lines.
Point = (1,-4).
One point = (2,0).
Other point = (0,-8).
As we know that,
⇒ Slope of line = m = (y₂ - y₁)/(x₂ - x₁).
⇒ Slope of line = m = (- 8 - 0)/(0 - 2).
⇒ Slope of line = m = (-8)/(-2) = 4.
As we know that,
Equation of line.
⇒ (y - y₁) = m(x - x₁).
⇒ (y - (-4)) = 4(x - 1).
⇒ (y + 4) = 4(x - 1).
⇒ y + 4 = 4x - 4.
⇒ 4x - 4 - y - 4 = 0.
⇒ 4x - y - 8 = 0.
