Question

Solve the following....
$5x+3y=7\\3x-5y=-23$

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

let's solve ~

The given equations are :

$\qquad \tt \dashrightarrow \:5x + 3y = 7 \: \: \: \: \: \: \: \: \: \: \: \: - (1)$

and

$\qquad \tt \dashrightarrow \:3x - 5y = - 23 \: \: \: \: \: \: - (2)$

Now, let's multiply equation (1) by 5 and equation (2) by 3 ~

we will get the results as :

$\qquad \tt \dashrightarrow \:25x + 15y = 35 \: \: \: \: - (3)$

$\qquad \tt \dashrightarrow \:9x - 15y = - 69 \: \: \: - (4)$

Now, add equation (3) and (4) :

$\qquad \tt \dashrightarrow \:25x + \cancel{ 15y} + 9x - \cancel{15y }= 35 + ( - 69)$

$\qquad \tt \dashrightarrow \:34x = - 34$

$\qquad \tt \dashrightarrow \:x = - 1$

Now, since we got the value of x, let's evaluate y~ by using equation (1) :

$\qquad \tt \dashrightarrow \:5x + 3y = 7$

$\qquad \tt \dashrightarrow \:5( - 1)+ 3y = 7$

$\qquad \tt \dashrightarrow \:3y - 5 = 7$

$\qquad \tt \dashrightarrow \:3y = 12$

$\qquad \tt \dashrightarrow \:y = 4$

Hence, value of y is 4

I hope you understood the whole procedure ~

Answer 2

Hello ~

My name is Irxdscent, and I will be answering your question today! :D

$\sf{5x \: + \: 3y = 7}$

⇢ Explanation :-

• Subtract $\bold{\underline{3y}}$ from both sides.

        $\bold{5x \: + \: 3y \: - \: 3y = 7 \: - \: 3y}$

• Simplify

        $\bold{5x = 7 \: - \: 3y}$

• Divide both sides $\bold{\underline{5}}$

        $\bold{\frac{5x}{5} = \frac{7}{5} \: - \:\frac{3y}{5}}$

• Simplify

        $\bold{x =\frac{7 \: - \: 3y}{5}}$

$\sf{3x \: - \: 5y = -23}$

⇢  Explanation :-

• Add $\bold{\underline{5y}}$ to both sides.

        $\bold{3x \: - \: 5y \: + \: 5y = -23 \: + \: 5y}$

• Simplify

        $\sf{3x = -23 \: + \: 5y}$

• Divide both sides by $\bold{\underline{3}}$

        $\bold{\frac{3x}{3} = -\frac{23}{3} \: + \: \frac{5y}{3}}$

• Simplify:

        $\bold{x = \frac{-23 \: + \: 5y}{3}}$

Hope It Helps! ~

~ Learn With Lrxdscent ~

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