Question

What is the solution of the system of equations?

5/3x−2y=−2
−x+y=2



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Answer 1

-x+y=2
y=2+x

5/3*x-2y=-2
5/3*x- 2 (2+x)= -2
5/3*x-4-2x=-2
5/3x -2x=4-2
x(5/3-2)=2
x(5/3-6/3)=6/3
x*(-1/3)=6/3
-x=6
x=-6
y=x+2
y=-6+2
y=-4

Answer 2

The solution of the given system of equation is (-6,-4)

Explanation:

Given system of equations
`(5)/(3)x-2y=-2 \\\\-x+y=2`

We have to solve the given system of equation

Consider the given system

`(5)/(3)x-2y=-2` .........(1)

`-x+y=2` .......(2)

We first simplify the equation (1) , we have

Multiply whole equation by 3,

`5x-6y=-6` ...........(3)

Multiply equation (2) by 5 , we have

`-5x+5y=10` ..........(4)

Now add equation (3) and (4) , we have

`5x-6y+(-5x+5y)=-6+10`

`5x-6y-5x+5y=4`

`-y=4`

`y=-4`

Substitute y = - 4 in (2) , we get

`-x+(-4)=2`

`\Rightarrow -x=2+4=6`

[tex]\Rightarrow x=-6[/tex]

Thus, x = -6 and y = -4

The solution of the given system of equation is (-6,-4)