Question

Solve the simultaneous linear equation 2x+5y=11, 7x+4y=2​

Answer 1

x = -
`(34)/(27)` and y =
`(73)/(27)`

Explanation:

2x + 5y = 11

7x + 4y = 2

Let's try elimination here since we have a system of equations:

-7(2x + 5y = 11) = -14x - 35y = -77

and

2(7x + 4y = 2) = 14x + 8y = 4

The x's cancel out now so let's combine the two equations:

-35 + 8 = -27

-77 + 4 = -73

-27y = -73

y =
`(73)/(27)`

Now that we have y's value, let's plug that value in for y in the other equation. You may choose whichever equation you want to solve for x but it is recommended to use the easiest one. (Since this value is complicated, it won't really matter.)

2x + 5(
`(73)/(27)`) = 11

2x +
`(365)/(27)` = 11

2x = -
`(68)/(27)`

x = -
`(34)/(27)`

To check and make sure you have the correct values, plug both values into the orginal equation and make sure the equation is true.

Answer 2

`{\tt{2x + 5y = 11}}`

`{\tt{7x + 4y = 2}}`

`\: \:`

`{\tt{2x = 11 - 5y}}`

`{\tt{7x = 2 - 4y}}`

`\: \:`

`{\tt{x = ( 11 - 5y ) ÷ 2}}`

`{\tt{x = (11)/(2) - (5)/(2) y}}`

`\: \:`

`{\tt{x = ( 2 - 4y ) ÷ 7}}`

`{\tt{x = (2)/(7) - (4)/(7) y}}`

`\: \:`

_____________________

`\: \:`

`\: \: \: \: \: \: {\tt{ (11)/(2) - (5)/(2) y = (2)/(7) - (4)/(7) y\: \: ( *14)}}`

`\: \: \: \: {\tt{77 - 35y = 4 - 8y}}`

`{\tt{ - 35y + 8y = 4 - 77}}`

`\: \: \: \: \: \: \: \: \: \: \: {\tt{ - 27y = - 73}}`

`\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\tt{y = (73)/(27) }}`

`\: \:`

SUBSTITUTION

`\: \:`

`{\tt{x = (2)/(7) - (4)/(7) * (73)/(27) }}`

`{\tt{x = - (34)/(27) }}`

`\: \:`