Question

Х+у= 9
2x – Зу = 8
someone plz solve

Answer 1

Explanation:

Given,

x + y = 9

2x - 3y = 8

Using substitution method:

In this method , a variable is expressed in terms of another variable from one equation and it is substituted in the remaining equation.

`\mathsf{x + y = 9}`

Move y to right hand side and change it's sign

⇒
`\mathsf{x = 9 - y}`⇔equation ( i )

Now, put the value of X from equation ( i )

⇒
`\mathsf{ 2 (9 - y) - 3y = 8}`

Distribute 2 through the parentheses

⇒
`\mathsf{18 - 2y - 3y = 8}`

Collect like terms

⇒
`\mathsf{18 - 5y = 8}`

Move constant to right hand side and change it's sign

⇒
`\mathsf{ - 5y = 8 - 18}`

Calculate

⇒
`\mathsf{ - 5y = - 10}`

Divide both sides of the equation by -5

⇒
`\mathsf{ ( - 5y)/( - 5) = ( - 10)/( - 5) }`

Calculate

⇒
`\mathsf{y = 2}`

Now, Put the value of y in the equation ( i )

⇒
`x = 9 - 2`

Calculate the difference

⇒
`\mathsf{x = 7}`

Hence, x = 7 and y = 2

The possible solution of the system is the ordered pair ( x , y )

`\mathsf{(x \: , y \: ) = (7 , \: 2)}`

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

Check if the given ordered pair is the solution of the system of equation

⇒
`\mathsf{7 + 2 = 9}`

⇒
`\sf{2 * 7 - 3 * 2 = 8}`

Simplify the equalities

⇒
`\sf{9 = 9}`

⇒
`\mathsf{8 = 8}`

Since all of the equalities are true , the ordered pair is the solution of the system.

`\mathsf{ \underline{ \bold{(x \:, y \: ) = (7 \:, 2)}}}`

Hope I helped!

Best regards!!

Answer 2

Explanation:

x+y=9

x=9-y ----------(i)

Now in second eqn put the value of x

2x -3y=8

2(9-y) - 3y=8

18 - 2y - 3y=8

18-8=5y

10=5y

y=2

Then put the value of y in eqn (i)

x=9-y

x=9-2

x=7

I hope this will be helpful for you.