Given:
The system of equations is
[tex]y=2x[/tex]
[tex]y=-x+6[/tex]
To find:
The solution of given system of equations.
Solution:
we have,
[tex]y=2x[/tex] ...(i)
[tex]y=-x+6[/tex] ...(ii)
From (i) and (ii), we get
[tex]2x=-x+6[/tex]
[tex]2x+x=6[/tex]
[tex]3x=6[/tex]
Divide both sides by 3.
[tex]x=2[/tex]
Putting x=2 in (i), we get
[tex]y=2(2)[/tex]
[tex]y=4[/tex]
So, the solution is (2,4).
For [tex]y=2x[/tex],
x y
0 0
1 2
For [tex]y=-x+6[/tex],
x y
0 6
1 5
Plot these points on a coordinate plane and connect them by straight line as shown below.
From the below graph it is clear that both lines intersect each other at (2,4). So, the solution is (2,4).
Therefore, the solution of system of equations is (2,4).
