Question

2x+3y=13
-7x-y=20solve by substitution method​

Answer 1

Given

$\sf \: 2x + 3y = 13$

$\sf \: - 7x - y = 20$

To Find

Value of x and y

$\sf\huge {\underline{\underline{{Solution}}}}$

$\sf\implies 2x + 3y = 13 - - (1)$

$\sf\implies - 7x - y = 20 - - (2)$

To solve both Equations by substitution method.

How to solve:

step 1:Convert any of the Equation either in the form of x or y .

Step 2:After converting into form put this into another equation to find another Variable.

Step 3: Now ,if one variable found then again put /substitute into step 1.

From equation 1

$\sf \boxed{\red{\: x = \dfrac{13 - 3y}{2} } - - (3)}$

Now,put X's value into equation 2

$\sf\implies - 7 \bigg( \dfrac{13 - 3y}{2} \bigg) - y = 20$

$\sf\implies \dfrac{ -91 + 21y}{2} - y = 20$

$\sf\implies \dfrac{ - 91 + 21y - 2y}{2} = 20$

$\sf\implies \dfrac{ - 91 + 19y}{2} = 20$

Now,cross multiply to both sides

$\sf\implies - 91 + 19y = 2 \times 20$

$\sf\implies - 91 + 19y = 40$

$\sf\implies 19y = 40 + 91$

$\sf\implies 19y = 131$

$\sf\boxed{ \blue{\: y = \dfrac{131}{19} }}$

Now,put y's into Equation 3

$\sf\implies \: x = \dfrac{13 - 3y}{2}$

$\sf \large\implies \dfrac{13 - 3( \frac{131}{19} )}{2}$

$\sf\implies \dfrac{13 - \dfrac{393}{19} }{2}$

$\sf\implies \dfrac{247 - 393}{ \dfrac{19}{2} }$

$\sf\implies \: x = \dfrac{ - 146}{38} = - \dfrac{73}{19}$

$\sf\boxed{ \: \green{x = - \dfrac{73}{19}} }$

Check:

$\sf\implies 2x + 3y = \orange{13}$

Taking LHS

$\sf\implies 2 \bigg( - \dfrac{73}{19} \bigg) + 3 \bigg( \dfrac{131}{19} \bigg)$

$\sf\implies \dfrac{ - 146 + 393}{19}$

$\sf\implies \dfrac{247}{19} = \orange{13}$

Since,LHS = RHS(Verified)

Answer 2

Answer↓

$\frac{247}{19}$

=13