Question

How do you solve this system of equations: `15x + 4y = 2145 and x + y = 165`?

Answer 1

`x=135` and `y=30`

Explanation:

From second equation, `y=165-x`

Hence,

`15x+4*(165-x)=2145`

`15x+660-4x=2145`

`11x=1485`, so `x=135`

Thus, `y=165-135=30`

Answer 2

`(x,y)to(135,30)`

Explanation:

`15x+4y=2145to(1)`

`x+y=165to(2)`

`"from equation "(2)" we can express y in terms of x"`

`rArry=165-xto(3)`

`color(blue)"substitute "y=165-x" in equation "(1)`

`15x+4(165-x)=2145`

`rArr15x+660-4x=2145`

`rArr11x+660=2145`

`"subtract 660 from both sides"`

`11xcancel(+660)cancel(-660)=2145-660`

`rArr11x=1485`

`"divide both sides by 11"`

`(cancel(11) x)/cancel(11)=1485/11`

`rArrx=135`

`color(blue)"substitute "x=135" in equation "(3)`

`y=165-135=30`

`rArr"point of intersection "=(135,30)`