Question

Heya❤️​

Solve these equations for x and y :

3x - 7y = 5
7y - 3x = 7​

Answer 1

Answer:

$3x-7y=5,\:7y-3x=7\quad :\quad \mathrm{No\:Solution}$

Explanation:

$\begin{bmatrix}3x-7y=5\\ 7y-3x=7\end{bmatrix}$

$\black{\mathrm{Isolate}\:x\:\mathrm{for}\:3x-7y=5:}$

$3x-7y=5$

$\gray{\mathrm{Add\:}7y\mathrm{\:to\:both\:sides}}$

$3x-7y+7y=5+7y$

$\gray{\mathrm{Simplify}}$

$3x=5+7y$

$\gray{\mathrm{Divide\:both\:sides\:by\:}3}$

$\displaystyle\frac{3x}{3}=\frac{5}{3}+\frac{7y}{3}$

$\gray{\mathrm{Simplify}}$

$\displaystyle x=\frac{5+7y}{3}$

$\displaystyle\gray{\mathrm{Subsititute\:} x= \frac{5+7y}{3}}$

$\begin{bmatrix}7y-3\cdot \displaystyle\frac{5+7y}{3}=7\end{bmatrix}$

$\displaystyle \gray{\mathrm{Refine\:}7y-3\frac{5+7y}{3}=7}$

$-12=0$

$\red{-12=0\:\mathrm{\:is\:false,\:therefore\:the\:system\:of\:equations\:has\:no\:solution}}$

$\mathrm{No\:Solution}$

Answer 2

Answer:

No solution.

Explanation:

Given :

3 x - 7 y = 5

3 x = 5 + 7 y  ... ( i )

7 y - 3 x = 7

3 x = 7 y + 7  ... ( ii )

From ( i )  and  ( ii ) we have

5 + 7 y = 7 y + 7

7 y - 7 y = 7 - 5

0  = 2

It means x and y have no solution.