Finite Math and Applied Calculus (6th Edition)

$(6,6)$
To eliminate y, multiply both equations with numbers so the coefficient of y is $\pm 6:$ $\left\{\begin{array}{llll} 3x & -2y & =6 & /\times 3\\ 2x & -3y & =-6 & /\times(-2) \end{array}\right.$ $\left\{\begin{array}{llll} 9x & -6y & =18 & \\ -4x & +6y & =12 & \end{array}\right.$ ... add and solve ... $5x=30\qquad/\div 5$ $x=6$ Back substitute into one of the initial equations: $3x-2y=6$ $3(6)-2y=6\qquad /-18$ $-2y=-12\qquad /\div(-2)$ $y=6$ Solutions are ordered pairs (x,y): $(6,6)$ Check graphically by graphing both lines in the same window and determining the intersection (see image).