Answer
$$x=-5$$ $$y=3$$
Work Step by Step
Equation 1: $0.01x - 0.06y = -0.23$
Equation 2: $0.2x + 0.4y = 0.2$
Using equation 2, subtract $0.2x$ from both sides:
$$0.2x + 0.4y = 0.2$$ $$0.2x -0.2x+ 0.4y = 0.2-0.2x$$ $$0.4y = 0.2-0.2x$$
Divide both sides by $0.4$:
$$\frac{0.4y}{0.4} = \frac{0.2-0.2x}{0.4}$$ $$y = 0.5-0.5x$$
Substitute this equation to equation 1:
$$0.01x - 0.06(0.5-0.5x) = -0.23$$ $$0.01x - 0.03+0.03x= -0.23$$ $$0.04x-0.03=-0.23$$
Add $0.03$ to both sides:
$$0.04x-0.03+0.03=-0.23+0.03$$ $$0.04x=-0.20$$
Divide both sides by $0.04$:
$$\frac{0.04x}{0.04}=\frac{-0.20}{0.04}$$ $$x=-5$$
Substitute this value of $x$ to equation 2:
$$0.2x + 0.4y = 0.2$$ $$0.2(-5) + 0.4y = 0.2$$ $$-1 + 0.4y = 0.2$$
Add $1$ to both sides:
$$-1+1 + 0.4y = 0.2+1$$ $$0.4y = 1.2$$
Divide both sides $0.4$:
$$\frac{0.4y}{0.4} =\frac{1.2}{0.4}$$ $$y=3$$
Check using equation 1:
$$0.01x - 0.06y = -0.23$$ $$0.01(-5) - 0.06(3) = -0.23$$ $$-0.05 - 0.18 = -0.23$$ $$-0.23=-0.23$$