Question

Find the point of intersection for the pair of linear equations. {x+y=4y=3x−18

Answer 1

Explanation:

as you can see, the correct writing of a problem definition is very important.

what you wrote is probably not the original problem.

it could be

x + y = 4y

4y = 3x - 18

the other answer was dealing with that possibility.

but I suspect it was more like

x + y = 4

y = 3x - 18

I am going to solve this here now.

in any case, remember, the intersection point of 2 lines or any kinds of functions is the point (the x and the y value), that gives the same result for both functions, or rather in forms like this that make both equations true.

the second equation gives us already a definition for y that we can use directly in the first equating to solve for x :

x + (3x - 18) = 4

x + 3x - 18 = 4

4x = 22

x = 22/4 = 5.5

that we can use then e.g. in the original first equation to solve for y :

x + y = 4

5.5 + y = 4

y = -1.5

so, the intersection point is

(5.5, -1.5) or (5 ½, -1 ½)

Answer 2

`((54)/(5),(18)/(5))`

Explanation:

`\mathrm{For\ finding\ the\ point\ of\ intersection,\ simply\ solve\ the\ given\ simultaneous\ }\\\mathrm{equations.}\\\mathrm{Here\ we\ have\ two\ equations:}\\4y=x+y\\\mathrm{or,\ }x=3y...........(1)\\\mathrm{And\ the\ other\ one:}\\4y=3x-18....(2)\\\mathrm{Now\ we\ substitute}\ x=3y\ \mathrm{in\ equation(2),}\\4y=3(3y)-18\\\mathrm{or,\ }4y=9y-18\\\mathrm{or,\ }5y=18\\\therefore\ y=(18)/(5)\\\mathrm{Now\ }x=3y=3((18)/(5))=(54)/(5)\\`

`\mathrm{Hence\ the\ point\ of\ intersection\ is\ }(x,y)=((54)/(5),(18)/(5))`