Question

Solve the following simultaneous
3a+5b=26 ; a+5b=22
​

Answer 1

Given :-

• 3a + 5b = 26
• a + 5b = 22

To find :-

• Find the value of a and b

Solution :-

Solve it by elimination method

• 3a + 5b = 26 ---(i)
• a + 5b = 22 ----(ii)

Subtract both the equations

→ 3a + 5b - (a + 5b) = 26 - 22

→ 3a + 5b - a - 5b = 4

→ 2a = 4

→ a = 4/2

→ a = 2

Put the value of a in equation (ii)

→ a + 5b = 22

→ 2 + 5b = 22

→ 5b = 22 - 2

→ 5b = 20

→ b = 20/5

→ b = 4

Hence,

• Required values
• a = 2 and b = 4

Answer 2

$\boxed{\rm{\orange{Given \longrightarrow }}}$

• 3a+5b=26
• a+5b=22

$\boxed{\rm{\red{To\:Find\longrightarrow }}}$

• The values of a and b.

$\boxed{\rm{\pink{Explaination\longrightarrow }}}$

3a + 5b = 26 …(i)

a + 5b = 22 …(ii)

Subtracting equation (ii) from (i),

we get;

$\sf\blue{↬}$3a + 5b - (a + 5b) = 26 - 22

$\sf\pink{↬}$3a + 5b - a - 5b = 4

$\sf\green{↬}$2a = 4

$\sf\purple{↬}$a = 4/2

$\sf\orange{↬}$a = 2

Now,

Substituting $\green{ \underline{ \boxed{ \sf{ a=2}}}}$ in equation (ii),

we get;

$\sf\green{↬}$2 + 5b = 22

$\sf\red{↬}$5b = 22 – 2

$\sf\pink{↬}$5b = 20

$\sf\purple{↬}$b = $\dfrac{20}{5}$= 4

Hence,

• (a, b) = (2, 4) is the solution of the given simultaneous equations.

━━━━━━━━━━━━━━━━━━━━━━━━━━