Question

Simultaneous equations 5x+y=28 x+y=2

Answer 1

`\boxed{x=6.5} \\ \boxed{y=-4.5}`

Explanation:

5x + y = 28

x + y = 2

Subtract both equations. (eliminating y variable)

4x + 0 = 26

4x = 26

Divide both sides by 4.

x =
`(26)/(4)`

x = 6.5

Plug x as 6.5 in the second equation and solve for y.

6.5 + y = 2

Subtract 6.5 on both sides.

6.5 - 6.5 + y = 2 - 6.5

y = -4.5

Answer 2

`( (13)/(2) \:</strong><strong>,</strong><strong> - (9)/(2) )`

Explanation:

`5x + y = 28`

`x + y = 8`

Solve the equation for y by moving 'x' to R.H.S and changing its sign

`5x + y = 28`

`y = 2 - x`

Substitute the given value of y into the equation 5x + y = 28

`5x + 2 - x = 28`

Solve the equation for x

Collect like terms

`4x + 2 = 28`

Move constant to R.H.S and change its sign

`4x = 28 - 2`

Subtract the numbers

`4x = 26`

Divide both sides of the equation by 4

`(4x)/(4) = (26)/(4)`

Calculate

`x = (26)/(4)`

Reduce the numbers with 2

`x = (13)/(2)`

Now, substitute the given value of x into the equation y = 2 - x

`y = 2 - (13)/(2)`

Solve the equation for y

`y = - (9)/(2)`

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

`(x \: y) = ( (13)/(2) </strong><strong>,</strong><strong> \: - (9)/(2) )`

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Let's check if the given ordered pair is the solution of the system of equation:

plug the value of x and y in both equation

`5 * (13)/(2) - (9)/(2) = 28`

`(13)/(2) - (9)/(2) = 2`

Simplify the equalities

`28 = 28`

`2 = 2`

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

`(x \:</strong><strong>,</strong><strong> y \: ) = ( (13)/(2) \: </strong><strong>,</strong><strong> - (9)/(2))`

Hope this helps....

Best regards!!