Finite Math and Applied Calculus (6th Edition)

$( 1,1)$
Remove the fractions by multiplying the first equation with 6, the second with 4 (common denominators). $\left\{\begin{array}{llll} -4x & +3y & =-1 & \\ x & -4y & =-3 & /\times 4 \end{array}\right.$ ... we aim to eliminate x... $\left\{\begin{array}{llll} -4x & +3y & =-1 & \\ 4x & -16y & =-12 & \end{array}\right.$ ... add and solve ... $-13y=-13\qquad/\div(-13)$ $y=1$ Back substitute into one of the above equations: $x-4y=-3$ $x-4(1)=-3\qquad/+4$ $x=1$ Solutions are ordered pairs (x,y): $( 1,1)$ Check graphically by graphing both lines in the same window and determining the intersection (see image).