When I graph system of linear equations and try to find an intersection point it says no sign change why?

To have any meaning, the x variable must be in radians.
To find the solutions of this equation you can graph the functions
y_1=x*sin(x)
y_2=0.1
Graph the two functions and find the intersection points of the two.
Because the two functions are even F(-x)=F(x), it suffices to consider their intersections on the interval [0, + infinity[
There are many solutions (an infinite number of them)
See some screen captures below.
After the graphs are drawn, use the G-Solve feature to find the intersections.

In theory yes. If you have a function y=f(x) and another y=g(x), an intersection point of the graphs of the two functions, if it exists, is a point (x_i,y_i) such that f(x_i)=g(x_i).
Graphically this means that (x_i, f(x_i))=(x_i, g(x_i)): The two curves pass through the same point in the Cartesian plane.
Now consider f(x_i)=g(x_i). That is an equation in x_i, or lest us just drop the _i to shorten and write f(x)=g(x), or f(x)-g(x)=0.
If you can feed it to the SOLVER in EQN, the equation mode, and the calculator gives you the roots of the equation, then for each root x_i found you have an intersection point (x_i, f(x_i)), or (x_i, g(x_i)). You can use either function to calculate the y-value since the two functions are supposed to be equal at the root x_i.
However it is much simpler to do with a graphing calculator.

In theory yes. If you have a function y=f(x) and another y=g(x), an intersection point of the graphs of the two functions, if it exists, is a point (x_i,y_i) such that f(x_i)=g(x_i).
Graphically this means that (x_i, f(x_i))=(x_i, g(x_i)): The two curves pass through the same point in the Cartesian plane.
Now consider f(x_i)=g(x_i). That is an equation in x_i, or lest us just drop the _i to shorten and write f(x)=g(x), or f(x)-g(x)=0.
If you can feed it to the SOLVER in EQN, the equation mode, and the calculator gives you the roots of the equation, then for each root x_i found you have an intersection point (x_i, f(x_i)), or (x_i, g(x_i)). You can use either function to calculate the y-value since the two functions are supposed to be equal at the root x_i.
However it is much simpler to do with a graphing calculator.

1. No solutions: The system is incoherent, incompatible Example: 2x+3y=8 and 2x+3y= 15. The two lines are parallel and distinct.
2. One solution: There exits a pair of values (x,y) that satisfy both linear equations. The two lines on a Cartesian graph have one intersection point.
3. Infinite number of solutions: The two equations are one and the same (one is just multiplied by some constant). The graph of the two lines yields the same line. One is superposed on the other. Any ordered pair (x,y) that satify one equation (there is an infinity of such pairs) satisfies the other.
4. Two solutions: cannot happen because the two lines can either intersect once, be parallel, or superposed one on the other.
   

You have to use Y Editor to define functions on the both sides of the equation and then graph it. Finally option is F5: Intersection.
See captured images for equation 5x+10=-2x-7, y1=5x+10, y2=-2x-7 and x=-17/7

See image below

Try rewriting your equations in the equivalent forms that follow.
Y1=3-X
Y2=(1-X)/3

If you do not get a syntax error it means that you were not using the correct minus sign.
If the - is the first symbol after the equal sign you must use negation (-) or change sign key.
Similarly, after the division / key you must use the negation or change sign (-)

The intersection function on the t-nspire is meant to find the intersection of two graphs, not of the graph and an axis. The easiest way to do this is to set the equation equal to 0 and then use nSolve() to find the intercept.

You must have used the TRANSFRM application before. It remains in memory and takes over the graphing function from the native OS. You must unload it from memory.

1. Turn calculator ON
2. Press the [APPS] button.
3. Scroll Up (faster) or Scroll down till you see :Transfrm in the list of applications.
4. Highlight that line and press ENTER.
5. The new screen invites you to Uninstall or Continue
6. Press the number key that corresponds to the Uninstall option (1:Uninstall)
7. Return to your [Y=] editor screen to verify that the style lines have changed to the "normal" ones.

I am not quite sure what you are asking...

(1) if asking for graphing y= -2/3x+2, then press [diamond] [F1: Y=] type in .2/3x +2, see graph by [diamond][graph]

(2) if asking for graphing y= -2/3x+a, where a=3x, then first archive a=3x in Home screen by [home], type 3x [sto] a, then go back to y= menu, and type -2/3x+a in Y1

(3) if asking for graphing an equation that is dependent on 2 variables at the same time, use x-y-z axis (aka, change mode to graphing 3-D by [mode]graph [5:3D]) then enter desired equation in y= menu using Z function in terms of x and y aka z(x,y)= ...)