Question

Substitution
Method of x+ 2y- 7=0, 2x-y-4=0​

Answer 1

Answer:

ΔGiven,

Equations:-

x + 2y -7 = 0  ----------------(i)

 &,

 2x - y - 4 = 0  --------------(ii)

By seeing the equations we come to know that these are linear equations.

because they have power as 1 ;.(x ¹+ 2y¹ -7 = 0 ) 

Take eqn(i)

x + 2y -7 = 0 

⇒ 2y = 7 - x

⇒ y  = (7 - x)/2

To plot a line on graph we need atleast two points.

Substitute any random values for or y and get the points,

if x = 0 ; y = 7/2 = 3.5 

point: A(0, 3.5)

if y = 0 ; x   = 7 

point: B(7, 0)

plot the points  A(0, 3.5) & B(7, 0)  on graph and join the points AB.

So a line is formed AB. that is the graph of the equation(i).

(2). Take eqn(ii)

 2x - y - 4 = 0

⇒ y = 2x - 4

if y = 0;  x = 2

Point: P(2, 0)

if x = 0;  y = -4

point: Q(-4, 0)

Line PQ is formed by joining the points P and Q.

See the graph here in attachement.

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Answer 2

Given equations

$x+2y-7=0\\2x-y-4=0$

Now,

$x+2y-7=0\\\implies x = 7-2y$

Substituting x in the second equation, we get,

$2(7-2y) - y - 4 = 0\\\implies 14 - 4y-y-4=0\\\implies -5y=-10$

$\implies y = \dfrac{-10}{-5}$

$\implies \underline{\underline{y=2}}$

$\implies x = 7-2(2) \\= 7-4 \\=\underline{\underline{ 3}}$

$\boxed{\boxed{\bold{Therefore, \ the \ values \ of \ x \ and \ y \ are \ 2 \ and \ 3 \ respectively.}}}}$