Question

How do you solve the system of equations `3x - y = 3` and `x + 7y = 23`?

Answer 1

Solution: `x = 2 , y = 3`

Explanation:

`3x-y=3 ; (1) and x+7y=23 ; (2)` . Multiplying equation (2)

by `3` we get `3x+21y=69 ; (3)`. Subtracting equation (1) from

equation (3) we get `22y=66 or y = 66/22=3`. Putting `y=3`

in equation (1) we get `3x-3=3 or 3x = 6 or x=2`

Solution: `x = 2 , y = 3` [Ans]

Answer 2

`(x,y)to(2,3)`

Explanation:

`"using the method of "color(blue)"substitution"`

`3x-y=3to(1)`

`x+7y=23to(2)`

`"rearrange equation "(2)" to give x in terms of y"`

`rArrx=23-7yto(3)`

`color(blue)"substitute "x=23-7y" into equation "(1)`

`3(23-7y)-y=3`

`rArr69-21y-y=3`

`rArr69-22y=3`

`"subtract 69 from both sides"`

`cancel(69)cancel(-69)-22y=3-69`

`rArr-22y=-66`

`"divide both sides by "-22`

`(cancel(-22) y)/cancel(-22)=(-66)/(-22)`

`rArry=3`

`"substitute this value into equation "(3)`

`rArrx=23-(7xx3)=23-21=2`

`"point of intersection "=(2,3)`
graph{(y-3x+3)(y+1/7x-23/7)((x-2)^2+(y-3)^2-0.07)=0 [-10, 10, -5, 5]}