Question

Solve the system of equations by the addition method. 0.01x-0.08y=-0.1 0.2x+0.6y=0.2

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Santino

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In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
0.01x-0.08y=0.1,0.2x+0.6y=0.2

To make $\frac{x}{100}$ and $\frac{x}{5}$ equal, multiply all terms on each side of the first equation by $0.2$ and all terms on each side of the second by $0.01$ .
0.2\times 0.01x+0.2\left(-0.08\right)y=0.2\times 0.1,0.01\times 0.2x+0.01\times 0.6y=0.01\times 0.2

Simplify.
0.002x-0.016y=0.02,0.002x+0.006y=0.002

Subtract $0.002x+0.006y=0.002$ from $0.002x-0.016y=0.02$ by subtracting like terms on each side of the equal sign.
0.002x-0.002x-0.016y-0.006y=0.02-0.002

Add $\frac{x}{500}$ to $-\frac{x}{500}$ . Terms $\frac{x}{500}$ and $-\frac{x}{500}$ cancel out, leaving an equation with only one variable that can be solved.
-0.016y-0.006y=0.02-0.002

Add $-\frac{2y}{125}$ to $-\frac{3y}{500}$ .
-0.022y=0.02-0.002

Add $0.02$ to $-0.002$ by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.
-0.022y=0.018

Divide both sides of the equation by $-0.022$ , which is the same as multiplying both sides by the reciprocal of the fraction.
y=-\frac{9}{11}

Substitute $-\frac{9}{11}$ for $y$ in $0.2x+0.6y=0.2$ . Because the resulting equation contains only one variable, you can solve for $x$ directly.
0.2x+0.6\left(-\frac{9}{11}\right)=0.2

Multiply $0.6$ times $-\frac{9}{11}$ by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.
0.2x-\frac{27}{55}=0.2

Add $\frac{27}{55}$ to both sides of the equation.
0.2x=\frac{38}{55}

Multiply both sides by $5$ .
x=\frac{38}{11}

The system is now solved.
x=\frac{38}{11},y=-\frac{9}{11}

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