Chapter 4 - Section 4.1 - Solving Systems of Linear Equations in Two Variables - Exercise Set - Page 212: 55

Ordered Pair Solution $(7,-3)$

We have $$1)\frac{x+5}{2} = \frac{6-4y}{3}$$ $$2)\frac{3x}{5}= \frac{21-7y}{10}$$ From (2) $$(3)x=\frac{7}{2}-\frac{7}{6}y$$ Substituting (3) in (1) $$(\frac{7}{2}-\frac{7}{6}y+5)*3 = (6-4y)*2$$ $$\frac{21}{2}-\frac{7}{2}y+15 = 12-8y$$ $$\frac{9}{2}y=-\frac{27}{2}$$ $$y = -3$$ Solving for $x$ $$x=\frac{7}{2}-\frac{7}{6}*(-3)=7$$ Ordered Pair Solution $(7,-3)$