Question 149211
There are several methods to solve this system of linear equations. 
We could graph both lines and look for the intersection point.
Put both into slope-intercept form, {{{y=mx+b}}}, and then graph.
{{{-x+y=4}}} 
{{{y=x+4}}}
{{{ graph( 300, 300, -5, 5, -10, 10, x+4) }}}
{{{2x-5y=-14}}}
{{{-5y=-2x-14}}}
{{{y=(-2x-14)/(-5)}}}
{{{y=(2x+14)/5}}}
{{{ graph( 300, 300, -5, 5, -10, 10, x+4,(2x+14)/5) }}}
Looks like a solution exists at (-2,2).
Although this method worked for this system, it's not always clear what the exact answer is. 
The graphical method explains what you're really trying to do, find where lines intersect, if they do. 
We'll work it out using the substitution method, to get an exact answer.
1.{{{-x+y=4}}}
2.{{{2x-5y=-14}}}
Use eq. 1 to get the variable y as an expression with x.
1.{{{-x+y=4}}}
{{{y=x+4}}}
Now substitute this expression into eq. 2 and solve for x,
2.{{{2x-5y=-14}}}
{{{2x-5(x+4)=-14}}}
{{{2x-5x-20=-14}}}
{{{-3x=6}}}
{{{highlight(x=-2)}}}
Now back substitute into eq. 1 or 2 to solve for y,
{{{y=x+4}}}
{{{y=-2+4}}}
{{{highlight(y=2)}}}