Question

question - 3 2x-3y +6=0 2x+3y-18=0 solve by substitution method​.​

Answer 1

Question -

Solve the following pair of equations by substitution method -

2x-3y+6=0

2x+3y-18=0

Solution -

Given equations,

2x-3y+6=0......1)

And,

2x+3y-18=0

2x= 18-3y......2)

Substituting the value of 2x in equation 1) we will get -

$\implies2x - 3y + 6 = 0$

$\implies18 - 3y - 3y + 6 = 0$

$\implies18 - 6y + 6 = 0$

$\implies24 - 6y = 0$

$\implies6y = 24$

$\implies \: y = \frac{24}{6}$

$\implies \: y = 4$

Now,

Substituting the value of y in equation 2) we will get -

$\implies2x = 18 - 3y$

$\implies2x = 18 - 3 \times 4$

$\implies2x = 18 - 12$

$\implies2x = 6$

$\implies \: x = \frac{6}{2}$

$\implies \: x = 3$

Verification -

=>2x-3y+6=0

Putting the values of x and y

=>2×3-3×4+6=0

=>6-12+6=0

=>12-12=0

=>0=0

Also,

=>2x+3y-18=0

Putting the values of x and y

=>2×3+3×4-18=0

=>6+12-18=0

=>18-18=0

=>0=0

L. H. S =R. H. S

Verified,

Therefore the value of x is 3 and y is 4

Answer 2

Question -

Solve the following pair of equations by substitution method -

2x-3y+6=0

2x+3y-18=0

Solution -

Given equations,

2x-3y+6=0......1)

And,

2x+3y-18=0

2x= 18-3y......2)

Substituting the value of 2x in equation 1) we will get -

\implies2x - 3y + 6 = 0⟹2x−3y+6=0

\implies18 - 3y - 3y + 6 = 0⟹18−3y−3y+6=0

\implies18 - 6y + 6 = 0⟹18−6y+6=0

\implies24 - 6y = 0⟹24−6y=0

\implies6y = 24⟹6y=24

\implies \: y = \frac{24}{6}⟹y=

6

24

\implies \: y = 4⟹y=4

Now,

Substituting the value of y in equation 2) we will get -

\implies2x = 18 - 3y⟹2x=18−3y

\implies2x = 18 - 3 \times 4⟹2x=18−3×4

\implies2x = 18 - 12⟹2x=18−12

\implies2x = 6⟹2x=6

\implies \: x = \frac{6}{2}⟹x=

2

6

\implies \: x = 3⟹x=3

Verification -

=>2x-3y+6=0

Putting the values of x and y

=>2×3-3×4+6=0

=>6-12+6=0

=>12-12=0

=>0=0

Also,

=>2x+3y-18=0

Putting the values of x and y

=>2×3+3×4-18=0

=>6+12-18=0

=>18-18=0

=>0=0

L. H. S =R. H. S

Verified,

Therefore the value of x is 3 and y is 4