Skip to content
Systems of Equations
Lesson 6
0% complete

Lesson 6: Solving Systems

Find values satisfying all equations simultaneously.

A system solution is the ordered pair that makes every equation true. Use substitution or elimination to reduce two equations to one variable.

Key formula

{a1x+b1y=c1a2x+b2y=c2\begin{cases}a_1x+b_1y=c_1\\a_2x+b_2y=c_2\end{cases}

Worked example

{−5x+4y=18−x+y=5⇒(x,y)=(2,7)\begin{cases}-5x+4y=18\\-x+y=5\end{cases}\Rightarrow (x,y)=(2,7)

Checkpoint

Find x in {2x+2y=−22x−3y=38\text{Find }x\text{ in }\begin{cases}2x+2y=-2\\2x-3y=38\end{cases}

Recap

  • - Two equations define one intersection point when independent.
  • - Elimination is efficient with opposite coefficients.
  • - Always verify both values in both equations.
Previous lessonNext lessonExamplesPracticeTry in calculator

Track progress: 0/8 completed.