Question

(-2x+3y=8....(i)
( x+y=2.........(ii)
solve by elumination method and substitution​

Answer 1

ELIMINATION:

You can multiply the second equation by 2:

`\begin{cases}-2x+3y=8\\2x+2y=4\end{cases}`

And then add the two equations:

`(-2x+3y)+(2x+2y)=8+4 \iff 5y=12 \iff y=(12)/(5)=2.4`

And we deduce

`x=2-y = 2-2.4=-0.4`

SUBSTITUTION:

From the second equation, we derive

`x=2-y`

Plug this expression for x in the first equation:

`-2x+3y=8 \iff -2(2-y)+3y=8 \iff -4+2y+3y=8 \iff 5y=12`

And from here you proceed in the same way as above.

Answer 2

x = -2/5

y = 12/5

Explanation:

Substitution method;

-2x + 3y = 8 -----------(i)

x + y =2 -----------(ii)

x = 2 - y

substitute the value of x in equ (i)

(-2)* (2-y) + 3y = 8

-4 + 2y + 3y = 8

5y = 8 + 4

y = 12/5

substitute the value of y in equ (ii)

x + 12/5 = 2

x = 2 - 12/5

= 2*5/1*5 - 12/5

= 10 -12/5 = -2/5

Ans: x = -2/5

y = 12/5

elimination method:

-2x + 3y = 8 -----------(i)

x + y =2 -----------(ii)

(i) ====> -2x + 3y = 8

multiply equ (ii) by 2 ====> 2x + 2y = 4

add (i) and (ii) 5y = 12

y = 12/5

Substitute in equ (ii)

x + 12/5 = 2

x = 2 - 12/5

= 2*5/1*5 - 12/5

= 10 -12/5 = -2/5

Ans: x = -2/5

y = 12/5