Question

3x-4y=10
4x+3y=5
solve x and y by substitution method

Answer 1

Step-by-step explanation:

Given -

• 3x - 4y = 10
• 4x + 3y = 5

To Find -

• Value of x and y by substitution method

Now,

→ 3x - 4y = 10

→ 3x = 10 + 4y

→ x = 10 + 4y/3

Now,

Substituting the value of x on 4x + 3y = 5, we get :-

→ 4(10+4y/3) + 3y = 5

→ 40+16y/3 + 3y = 5

→ 40+16y+9y/3 = 5

→ 40 + 25y = 15

→ 25y = 15 - 40

→ 25y = -25

→ y = -1

Now,

Substituting the value of y on x = 10+4y/3, we get :-

→ x = 10 + 4(-1)/3

→ x = 10 - 4/3

→ x = 6/3

→ x = 2

Hence,

The value of x is 2 and y is -1.

Verification :-

• 3x - 4y = 10

→ 3(2) - 4(-1) = 10

→ 6 + 4 = 10

→ 10 = 10

LHS = RHS

And

• 4x + 3y = 5

→ 4(2) + 3(-1) = 5

→ 8 - 3 = 5

→ 5 = 5

LHS = RHS

Hence,

Verified...

It shows that our answer is absolutely correct.

Answer 2

Solution :

$\bigstar$Let suppose equation both, we get;

$\bullet\:\sf{3x-4y=10......................(1)}\\\bullet\sf{4x+3y=5........................(2)}$

$\underline{\boldsymbol{By\:Substitution\:Method\::}}}$

From equation (1),we get;

$\longrightarrow\tt{3x-4y=10}\\\\\longrightarrow\tt{3x=10+4y}\\\\\longrightarrow\tt{x=10+4y/3.....................(3)}$

Putting the value of x in equation (2),we get;

$\longrightarrow\tt{4\bigg(\dfrac{10+4y}{3} \bigg)+3y=5}\\\\\\\longrightarrow\tt{\dfrac{40+16y}{3} +3y=5}\\\\\longrightarrow\tt{40+16y+9y=15}\\\\\longrightarrow\tt{40+25y=15}\\\\\longrightarrow\tt{25y=15-40}\\\\\longrightarrow\tt{25y=-25}\\\\\longrightarrow\tt{y=-\cancel{25/25}}\\\\\longrightarrow\bf{y=-1}$

Putting the value of y in equation (3),we get;

$\longrightarrow\tt{x=\dfrac{10+4(-1)}{3} }\\\\\\\longrightarrow\tt{x=\dfrac{10+(-4)}{3}}\\\\\\\longrightarrow\tt{x=\dfrac{10-4}{3}}\\\\\longrightarrow\tt{x=\cancel{6/3}}\\\\\longrightarrow\bf{x=2}$

Thus;

The value will be x = 2 & y = -1 .