No.123 Systems with Decimals and Fractions
POINT
For decimals, multiply both sides by 10 or 100 to make integer coefficients. For fractions, multiply both sides by the least common multiple of the denominators to clear the fractions.
Solve the following system of equations.
Example
①
\(\begin{cases}0.3x+0.2y=0\\0.4x-0.5y=2.3\end{cases}\)
②
\(\begin{cases}\frac12x+\frac13y=\frac{13}{6}\\\frac23x-\frac14y=\frac32\end{cases}\)
① \((x,y)=(2,-3)\)
② \((x,y)=(3,2)\)
② \((x,y)=(3,2)\)
Try it yourself.
Solve the following system of equations.
PRACTICE 01
\(\begin{cases}0.2x+0.3y=1.3\\0.5x-0.2y=0.1\end{cases}\)
PRACTICE 02
\(\begin{cases}0.4x-0.1y=1.0\\0.2x+0.3y=1.4\end{cases}\)
PRACTICE 03
\(\begin{cases}\frac12x+\frac14y=2\\\frac13x-\frac12y=-\frac13\end{cases}\)
PRACTICE 04
\(\begin{cases}\frac23x+\frac15y=\frac{13}{5}\\\frac12x-\frac25y=-\frac15\end{cases}\)
1. \(x=\frac{29}{19},\ y=\frac{63}{19}\)
2. \(x=\frac{22}{7},\ y=\frac{18}{7}\)
3. \(x=\frac{11}{4},\ y=\frac52\)
4. \(x=\frac{30}{11},\ y=\frac{43}{11}\)