Question

solve the equations 2l-5b=-70 and -5l+10b=100 and find the values of l and b​

Answer 1

$\sf\large\purple{\underbrace{ Question : }}$

Solve the equations 2l - 5b = - 70 &

- 5l + 10b = 100 .

$\sf\large\purple{\underbrace{ Solution : }}$

★ Given that,

• 2l - 5b = - 70
• - 5l + 10b = 100

★ To find,

• Value of l & b.

★ Let,

☯ To get the value of l & b we can do two methods. These methods are :

1. Substitution method.
2. Elimination method.

I choose " Elimination method " to do this problem.

★ So,

The equations are :

• 2l - 5b = - 70 ..... ➊
• - 5l + 10b = 100 ..... ➋

★ Now,

• Multiply equation ➊ with 5.
• Multiply equation ➋ with 2.

★ We get,

$\bf\:\implies 10l - 25b = - 350$

$\bf\:\implies - 10l + 20b = 200$

• From these equations, we get

$\bf\:\implies - 5b = - 150$

$\bf\:\implies b = \frac{- 150}{- 5}$

$\bf\:\implies b = 30$

$\boxed{ Hence, b = 30 }$

• Substitute the value of b in ➊.

$\bf\:\implies 2l - 5(30) = - 70$

$\bf\:\implies 2l - 150 = - 70$

$\bf\:\implies 2l = - 70 + 150$

$\bf\:\implies 2l = 80$

$\bf\:\implies l = \frac{80}{2}$

$\bf\:\implies l = 40$

$\boxed{ Hence, l = 40 }$

★ Verification,

☯ Substitute the values of l & b in any equations.

$\bf\:\implies 2(40) - 5(30)$

$\bf\:\implies 80 - 150$

$\bf\:\implies - 70$

Hence, LHS = RHS.

★ It is verified.

$\underline{\boxed{\tt{\blue{ \therefore l = 40 , b = 30}}}}\:\orange{\bigstar}$