Question

solve the pair of linear eqautio graphically x-y+1=0 and 2x+2y-12=0​

Answer 1

Given

We have given two pair of linear equations

x-y+1=0 & 2x+2y-12=0

To find

We have to find value of x and y

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

➙ x-y+1=0

➙x=y-1

At x

y=0

➙x= -1

At y= 1

➙x= 1-1=0

➙x=0

At y=2

➙x= 2-1=1

➙x=1

Plot points in table

$\large \boxed{\begin{tabular}{c|c|c|c}x & -1 & 0 & 1 \\ \cline{1-4} y & 0 & 1 & 2\end{tabular}}$

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2x+2y-12=0

➙2x+2y=12

Taking 2 common

➙2(x+y)=12

➙x+y=6

➙x= 6-y

At y=0

➙x=6

At y= 1

➙x= 6-1=5

At y= 2

➙x= 6-2=4

Plot points in table

$\large \boxed{\begin{tabular}{c|c|c|c}x & 6 & 5 & 4 \\ \cline{1-4} y & 0 & 1 & 2\end{tabular}}$

Note :As this is not visible on app kindly see from web .

From graph 3 we see that the lines intersect at 2 & 4

So,x will be 2 and y will be 4

Hence,the value of x= 2 ,y=4.

Check:

➙2x+2y-12=0

➙2(2)+2(4)-12

➙4+8-12

➙12-12=0

Answer 2

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$\boxed{\sf{ Equation\:(1)\: \longrightarrow \: x - y + 1 \:=\: 0 }}$

$\boxed{\sf{Equation\:(2)\: \longrightarrow \: 2x + 2y - 12 \:=\: 0}}$

$\therefore$ Equation ( 1 ) becomes =

ㅤㅤㅤ➪ x - y + 1 = 0

ㅤㅤㅤ➪ x + 1 = 0 + y

ㅤㅤㅤ➪ x = y - 1

Let ,

ㅤㅤㅤy = 1

•°• ㅤ➪ x = y - 1

ㅤㅤ ➪ x = 1 - 1

ㅤㅤ ➪ x = 0

Again Let ,

ㅤ ㅤㅤy = 3

•°•ㅤ ➪ x = y - 1

ㅤㅤ ➪ x = 3 - 1

ㅤㅤ ➪ x = 2

$\boxed{\sf{\therefore \:Coordinates\: of \: x - y + 1 \:=\: 0 \: are \: ( 0 , 1 ) \: and \: ( 2 , 3 )}}$

Now ,

ㅤㅤㅤ Equation ( 2 ) becomes =

ㅤㅤㅤ➪ 2x + 2y = 12

ㅤㅤㅤ➪ 2x = 12 - 2y

ㅤㅤㅤ➪ x = $\sf{\dfrac{ 12 - 2y }{2}}$

Let ,

ㅤㅤㅤy = 1

•°• ㅤ➪ x = $\sf{\dfrac{ 12 - 2y }{2}}$

ㅤㅤ ➪ x = $\sf{\dfrac{ 12 - 2 × 1 }{2}}$

ㅤㅤ ➪ x = $\sf{\dfrac{ 12 - 2 }{2}}$

ㅤㅤ ➪ x = $\sf{\dfrac{ 10 }{2}}$

ㅤㅤ ➪ x = 5

Again Let ,

ㅤㅤㅤy = 2

•°• ㅤ➪ x = $\sf{\dfrac{ 12 - 2y }{2}}$

ㅤㅤ ➪ x = $\sf{\dfrac{ 12 - 2 × 2 }{2}}$

ㅤㅤ ➪ x = $\sf{\dfrac{ 12 - 4 }{2}}$

ㅤㅤ ➪ x = $\sf{\dfrac{ 8 }{2}}$

ㅤㅤ ➪ x = 4

$\boxed{\sf{\therefore \:Coordinates\: of \: 2x + 2y - 12 \:=\: 0 \: are \: ( 5 , 1 ) \: and \: ( 4 , 2 )}}$

Graph is in the attachment*

$\boxed{\text{Note* Slide to view full answer }}$

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