Question

Check whether the pair of equations 2x + y - 5 = 0 and 3x - 2y -4 = 0 are consistent or com
graphically, find the solution if the equations are consistent.




with table
observation
verification
conclusion ​

Answer 1

Answer:-

(x,y) = (2,1)

Explanation:-

Given:-

Equations are:

2x+y-5 = 0 .....(1)

3x-2y-4 = 0 .....(2)

To Find:-

In equation (1)

• $a_1 = 2$
• $b_1 = 1$
• $c_1 = -5$

In equation (2)

• $a_2 = 3$
• $b_2 = -2$
• $c_2 = -4$

If the equations are consistent, then

Equations have infinte solutions

$\boxed{\bold{\dfrac{a_1}{a_2}= \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}}}$

(or)

Equations have a unique solution:-

$\boxed{\bold{\dfrac{a_1}{a_2}≠ \dfrac{b_1}{b_2} }}$

Let's verify the equations

$\dfrac{a_1}{a_2} = \dfrac{2}{3}$

$\dfrac{b_1}{b_2} = \dfrac{-1}{2}$

Here,

$\bold{\dfrac{a_1}{a_2}≠ \dfrac{b_1}{b_2} }$

Hence, the equations have unique solution

From equation (1)

${\rightarrow}\: 2x+y-5 = 0$

${\rightarrow}\: 2x+y = 5$

${\rightarrow}\: y = 5-2x$

Put, value of Y in equation (2)

${\rightarrow}\: 3x-2(5-2x) -4= 0$

${\rightarrow}\: 3x-10+4x -4 = 0$

${\rightarrow}\: 7x-14 = 0$

${\rightarrow}\: 7x = 14$

$\bold{{\rightarrow}\: x = 2}$

Now,

${\rightarrow}\: y = 5-2x$

${\rightarrow}\: y = 5-2(2)$

${\rightarrow}\: y = 5-4$

${\rightarrow}\: y = 1$

Hence, the point where both equations meet = (2,1)

Answer 2

Answer:

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