Question

5x+6y=11 2x-y=1 Solve by substitution method
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Answer 1

Answer:

5x−6y=2 ------- (1)

6x−5y=9 ------ (2)

From equation 1:

6y=5x−2

y=

6

5x−2

Substitute the value of y in equation 2 :

6x−5y=9

6x−5(

6

5x−2

)=9

36x−25x+10=54

11x=54−10

X=

11

44

=4

Now, Substitute x=4 in equation 1 :

5x−6y=2

5×4−6y=2

20−2=6y

18=6y

y=

6

18

=3

Therefore the solution is: x=4 and y=3

Answer 2

Step-by-step explanation:

Let

${\boxed {5x+6y=11}}........(1)$

${\boxed{2x-y=1}}........(2)$

From equation (1)

${:}\longrightarrow$$5x+6y=11$

${:}\longrightarrow$$6y=11-5x$

${:}\longrightarrow$$y={\frac {11-5x}{6}}..........(3)$

Substitute the value of y in Equation (2)

${:}\longrightarrow$$2x- ({\frac {11-5x}{6}}=1$

${:}\longrightarrow$${\frac {12x-(11-5x)}{6}}=1$

${:}\longrightarrow$${\frac {12x-11+5x}{6}}=1$

${:}\longrightarrow$${\frac {17x-11}{6}}=1$

${:}\longrightarrow$$17x-11=6$

${:}\longrightarrow$$17x=6+11$

${:}\longrightarrow$$17x=17$

${:}\longrightarrow$$x={\frac {17}{17}}$

${:}\longrightarrow$${\underline{\boxed{\bf {x=1}}}}$

Substitute the value of x in Equation (3)

${:}\longrightarrow$$y={\frac{11-5x}{6}}$

${:}\longrightarrow$$y={\frac {11-5 (1)}{6}}$

${:}\longrightarrow$$y={\frac {11-5}{6}}$

${:}\longrightarrow$$y={\frac {6}{6}}$

${:}\longrightarrow$${\underline{\boxed{\bf {y=1}}}}$

$\therefore$${\underline{\boxed{\bf {(x,y)=(1,1)}}}}$