Chapter 4 - Section 4.1 - Solving Systems of Linear Equations in Two Variables - Exercise Set - Page 212: 28

Ordered pair solution $(-3, 2)$

We have $$(1) \frac{2}{3}x+\frac{1}{4}y=-\frac{3}{2}$$ $$(2)\frac{1}{2}x-\frac{1}{4}y=-2$$ Adding (1) + (2) $$\frac{2}{3}x + \frac{1}{2}x+\frac{1}{4}y-\frac{1}{4}y=-\frac{3}{2}-2$$ $$\frac{7}{6}x=-\frac{7}{2}$$ $$x=-3$$ Solving for $y$ $$y =(-\frac{3}{2} -\frac{2}{3}*(-3))*4= 2$$ Ordered pair solution $(-3, 2)$