No.120 Elimination by Subtraction

POINT

When both the sign and coefficient are the same, subtract one equation from the other to eliminate that variable.

Solve the following system of equations.

Example

①

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

②

\(\begin{cases}-3x-y=5\\-3x+2y=8\end{cases}\)

① \((x,y)=(-1,3)\)
② \((x,y)=(-2,1)\)

Try it yourself.

Solve the following system of equations.

PRACTICE 01

\(\begin{cases}2x+y=7\\-x+y=1\end{cases}\)

PRACTICE 02

\(\begin{cases}3x-2y=4\\x-2y=-2\end{cases}\)

PRACTICE 03

\(\begin{cases}-2x+3y=11\\x+3y=5\end{cases}\)

PRACTICE 04

\(\begin{cases}4x+y=9\\2x+y=5\end{cases}\)

PRACTICE 05

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

PRACTICE 06

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

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

2. \(x=3,\ y=\frac52\)

3. \(x=-2,\ y=\frac73\)

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

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

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