Question

How do solve the following linear system?: `7x-2y=8 , 3x – 4y = 7`?

Answer 1

By substitution or by elimination

Explanation:

you are given a 2 equation and you need to find both x and y

`{(7x-2y=8), (3x-4y=7) :}`

there are two solutions and they have both the same answer. you will just choose what is easier.

By substitution
first let's find the value of x in first equation

`7x-2y=8`

`7x=8+2y ->` transpose `2y` to other side of equation to leave `7x`

`x= (8+2y)/7 ->` divide both side by `7`

then we have the x value

substitute your answer (the value of `x`) to next equation

`3 * ((8+2y)/7) - 4y = 7`

`(24+6y)/7 - 4y = 7`

`(24+6y)/7 - 4y = 7 | * (7)`

`24+6y-28y=49`

`-22y=49-24`

`-22y=25`

`y=-25/22`

To find the value of `x` just substitute the first equation by the value of `y`.

BY ELIMINATION

`{(7x-2y=8), (3x-4y=7) :}`

Think of how to eliminate any one of the variables.

i think that if we multiply the first equation by `-2`, `y` will be cancelled.

`{((7x-2y=8) | * (-2)), (3x-4y=7):}`

`-14x + 4y = -16`
`" "3x - 4y =7`

Add the two equations to get

`-14x + cancel(4y) + 3x - cancel(4y) = -16 + 7`

`-11x=-9 ->` divide both sides by `-11`

`x=9/11`

To know the value of `y`, substitute the value of `x` in one of the equation.

`3x-4y=7`

`3 * (9/11) - 4y=7`

`27/11 - 4y = 7`

`-4y=7 - 27/11`

`-4y=50/11 ->` divide both sides by `-4`

`y=-25/22`