# Chapter 3 - Section 3.1 - Systems of Two Equations in Two Unknowns - Exercises: 9

$( 0,-2)$

#### Work Step by Step

Remove the fractions by multiplying the first equation with 6, the second with 4 (common denominators). $\left\{\begin{array}{llll} 2x & -3y & =6 & \\ x & +4y & =-8 & /\times(-2) \end{array}\right.$ ... we aim to eliminate x... $\left\{\begin{array}{llll} 2x & -3y & =6 & \\ -2x & -8y & =16 & /\times(-2) \end{array}\right.$ ... add and solve ... $-11y=22\qquad/\div(-11)$ $y=-2$ Back substitute into one of the above equations: $x+4y=-8$ $x+4(-2)=-8\qquad/+8$ $x=0$ Solutions are ordered pairs (x,y): $( 0,-2)$ Check graphically by graphing both lines in the same window and determining the intersection (see image).

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