No.121 Match Coefficients First
POINT
Multiply both sides of an equation by a suitable number to match the coefficient of \(x\) or \(y\) (the signs may differ). Then eliminate a variable using column-style addition or subtraction.
Solve the following system of equations.
Example
①
\(\begin{cases}3x+2y=13\\4x-3y=6\end{cases}\)
②
\(\begin{cases}3x-2y=-11\\4x+5y=16\end{cases}\)
① \((x,y)=(3,2)\)
② \((x,y)=(-1,4)\)
② \((x,y)=(-1,4)\)
Try it yourself.
Solve the following system of equations.
PRACTICE 01
\(\begin{cases}2x+3y=7\\3x-2y=4\end{cases}\)
PRACTICE 02
\(\begin{cases}4x+y=11\\3x-2y=4\end{cases}\)
PRACTICE 03
\(\begin{cases}5x-2y=8\\3x+4y=14\end{cases}\)
PRACTICE 04
\(\begin{cases}2x-5y=-1\\3x+2y=12\end{cases}\)
PRACTICE 05
\(\begin{cases}3x+4y=18\\5x-2y=4\end{cases}\)
PRACTICE 06
\(\begin{cases}4x-3y=-2\\2x+5y=16\end{cases}\)
1. \(x=2,\ y=1\)
2. \(x=\frac{26}{11},\ y=\frac{17}{11}\)
3. \(x=\frac{30}{13},\ y=\frac{23}{13}\)
4. \(x=\frac{58}{19},\ y=\frac{27}{19}\)
5. \(x=2,\ y=3\)
6. \(x=\frac{19}{13},\ y=\frac{34}{13}\)