Answer
$$x=\frac{47}{5}$$ $$y=\frac{48}{5}$$
Work Step by Step
Equation 1: $x-\frac{2}{3}y=3$
Equation 2: $-2x + 3y = 10$
Multiply equation 1 by $2$:
$$[x-\frac{2}{3}y=3]\cdot2$$ $$2x-\frac{4}{3}y=6$$
We can call this equation 1'.
Add equation 1' to equation 2:
$$2x-\frac{4}{3}y=6$$ $$+$$ $$-2x + 3y = 10$$ $$=$$ $$\frac{5}{3}y=16$$
Multiply the whole equation by $3$:
$$[\frac{5}{3}y=16]\cdot3$$ $$5y=48$$
Divide both sides by $5$:
$$\frac{5y}{5}=\frac{48}{5}$$ $$y=\frac{48}{5}$$
Substitute this value of $y$ to equation 2:
$$-2x + 3y = 10$$ $$-2x + 3(\frac{48}{5}) = 10$$ $$-2x + \frac{144}{5} = 10$$
Subtract $\frac{144}{5}$ from both sides:
$$-2x + \frac{144}{5} -\frac{144}{5}= 10-\frac{144}{5}$$ $$-2x =\frac{50}{5}-\frac{144}{5}$$ $$-2x =-\frac{94}{5}$$
Divide both sides by $-2$:
$$\frac{-2x}{-2} =\frac{-\frac{94}{5}}{-2}$$ $$x=-\frac{94}{5}\cdot-\frac{1}{2}$$ $$x=\frac{94}{10}$$ $$x=\frac{47}{5}$$
Check using equation 1:
$$x-\frac{2}{3}y=3$$ $$\frac{47}{5}-\frac{2}{3}(\frac{48}{5})=3$$ $$\frac{47}{5}-\frac{96}{15}=3$$ $$\frac{141}{15}-\frac{96}{15}=3$$ $$\frac{45}{15}=3$$ $$3=3$$
