No.122 Substitution Method

POINT

Substitute the expression for one variable into the other equation, then solve the resulting equation in one variable.

Solve the following system of equations.

Example

①

\(\begin{cases}5x+y=-6\\y=-4x+3\end{cases}\)

②

\(\begin{cases}x=3y-1\\3x+2y=19\end{cases}\)

① \((x,y)=(-9,39)\)
② \((x,y)=(5,2)\)

Try it yourself.

Solve the following system of equations.

PRACTICE 01

\(\begin{cases}y=2x+1\\3x-y=4\end{cases}\)

PRACTICE 02

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

PRACTICE 03

\(\begin{cases}y=-x+5\\4x+y=11\end{cases}\)

PRACTICE 04

\(\begin{cases}x=2y-3\\x+y=6\end{cases}\)

PRACTICE 05

\(\begin{cases}y=3x-2\\2x+y=13\end{cases}\)

PRACTICE 06

\(\begin{cases}x=-y+4\\3x-2y=7\end{cases}\)

1. \(x=5,\ y=11\)

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

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

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

5. \(x=3,\ y=7\)

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