to solve this system of linear equations we need a little trick called elimination steps are below
we are given the following system of equations
[tex] - 4x - 15y = - 17[/tex]
[tex] - x + 5y = - 13[/tex]
if you look at the x variables in both equations you can see that we can easily eliminate them by multiplying the bottom equation by -4 as so
[tex] - 4x - 15y = - 17[/tex]
[tex] - 4( - x + 5y = - 13)[/tex]
simplify and we get
[tex] - 4x - 15y = - 17[/tex]
[tex]4x - 20y = 52[/tex]
now we can combine like terms on each side with the x's cancelling and get
[tex] - 35y = 35[/tex]
now divide off -35
[tex]y = - 1[/tex]
great now we can go back to our original system and pick a equation and substitute y back in to find x lets use
[tex] - x + 5y = 13[/tex]
so now we substitute y and get
[tex] - x + 5( - 1) = 13[/tex]
[tex] - x - 5 = 13[/tex]
[tex] - x = 17[/tex]
[tex]x = - 17[/tex]
now we put x and y into one coordinate (x,y)
so now our FINAL ANSWER IS
(-17,-1)
