No.119 Elimination by Addition

POINT

When the coefficients have the same absolute value but opposite signs, add the two equations to eliminate that variable.

Solve the following system of equations.

Example

①

\(\begin{cases}-2x+3y=19\\2x-5y=-29\end{cases}\)

②

\(\begin{cases}2x-y=5\\-3x+y=-7\end{cases}\)

① \((x,y)=(-2,5)\)
② \((x,y)=(2,-1)\)

Try it yourself.

Solve the following system of equations.

PRACTICE 01

\(\begin{cases}-x+3y=7\\x+2y=3\end{cases}\)

PRACTICE 02

\(\begin{cases}2x-y=8\\-2x+3y=0\end{cases}\)

PRACTICE 03

\(\begin{cases}-3x+2y=1\\3x+y=8\end{cases}\)

PRACTICE 04

\(\begin{cases}4x-3y=5\\-4x+y=-7\end{cases}\)

PRACTICE 05

\(\begin{cases}-2x+5y=4\\2x+y=8\end{cases}\)

PRACTICE 06

\(\begin{cases}5x+2y=1\\-5x+3y=9\end{cases}\)

1. \(x=-1,\ y=2\)

2. \(x=6,\ y=4\)

3. \(x=\frac53,\ y=3\)

4. \(x=2,\ y=1\)

5. \(x=3,\ y=2\)

6. \(x=-\frac35,\ y=2\)