Question

2x-3y=21 -6x+2y=7 I also need to be shown how to solve this

Answer 1

`\underline{\bigstar{\sf\ \ Answer :-}}`

Given two equations of two variables x and y

Now lets solve it by elemination method !

`:\implies\sf 2x-3y=21--------(1)\\ \\ \\ :\implies\sf -6x+2y=7-------(2)\\ \\ \\ \sf Eleminate\ (x) \\ \\ \\ \it Multiply\ first \ equation \ with \ 3\ \ \ and \ 2nd \ \ with \ 1 \\ \\ \\ :\implies\sf (2x-3y=21)* 3 \\ \\ \\ :\implies\sf (-6x+2y=7)* 1\\ \\ \\ :\implies\sf 6x-9y=63------(3) \\ \\ \\ :\implies\sf -6x+2y=7-----(4)\\ \\ \\ \it\ \ Add \ equation\ 3\ \ and \ 4\\ \\ \\ :\implies\sf 6x-9y=63+ (-6x+2y= 7)\\ \\ \\ :\implies\sf (6x-6x)+(-9y+2y) = 63+7\\ \\ \\ :\implies\sf 0-7y=70\\ \\ \\ :\implies\sf y= \cancel{(70)/(-7)}= - 10\\ \\ \\ :\implies\sf y= -10`

★ Now find the value of x

let's substitute the value of y in equation 4

`:\implies\sf -6x+2y=7\ \ \ \ \ \ (y= -10)\\ \\ \\ :\implies\sf -6x+2* (-10)=7\\ \\ \\ :\implies\sf -6x-20= 7\\ \\ \\ :\implies\sf -6x = 7+20 \\ \\ \\ :\implies\sf x= \cancel{(27)/(-6)}= (-9)/(2)`

`\underline{\textit{ \ \ So, \ the \ value \ of \ x\ and \ y }}`

`\bigstar{\boxed{\sf x= (-9)/(2)}}`

`\bigstar{\boxed{\sf\ y= (-10)}}`

Answer 2

(-9/2 , -10)

Explanation:

2x-3y=21

-6x+2y=7

Multiply the first equation by 3

3(2x-3y)=21*3

6x - 9y = 63

Add this to the second equation to eliminate x

6x - 9y = 63

-6x+2y=7

------------------

0x -7y = 70

Divide by -7

-7y/-7 = 70/-7

y = -10

Now find x

2x- 3y = 21

2x -3(-10) = 21

2x +30 =21

subtract 30 from each side

2x = 21-30

2x= -9

Divide by 2

x = -9/2

(-9/2 , -10)