The coordinates (x,y) are (3,2), If the graphs of [tex]2x+3y=12[/tex] and [tex]2x-y=4[/tex] are intersect.
Step-by-step explanation:
The given is,
[tex]2x+3y=12[/tex].................................(1)
[tex]2x-y=4[/tex]....................................(2)
Step:1
The values of x and y are obtained by elimination method,
Substrate the equation (1) and (2),
[tex]2x+3y=12[/tex]
[tex]2x-y=4[/tex]
( - )
Equation becomes,
[tex](2x-2x)+(3y+y)=(12-4)[/tex]
[tex](0)+(4y)=(8)[/tex]
[tex]4y=8[/tex]
[tex]y=\frac{8}{4}[/tex]
[tex]y=2[/tex]
From the equation (1),
[tex]2x+3y=12[/tex]
[tex]2x+3(2)=12[/tex]
[tex]2x+6=12[/tex]
[tex]2x=12-6[/tex]
[tex]x=\frac{6}{2}[/tex]
[tex]x=3[/tex]
Step:2
Check for solution,
[tex]2x-y=4[/tex]....................................(2)
Substitute the values of x = 3 and y = 2 in above equation,
[tex]2(3)-2=4[/tex]
[tex]6-2=4[/tex]
[tex]4=4[/tex]
Both sides are equal, so the x = 3 and y = 2 is correct answer
Result:
The coordinates (x,y) are (3,2), If the graphs of [tex]2x+3y=12[/tex] and [tex]2x-y=4[/tex] are intersect.
