Skip to content
Systems of Equations
Lesson 7
0% complete

Lesson 7: 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

{x+3y=7−x−2y=−5⇒(x,y)=(1,2)\begin{cases}x+3y=7\\-x-2y=-5\end{cases}\Rightarrow (x,y)=(1,2)

Checkpoint

Find x in {−x−y=10−x+2y=−14\text{Find }x\text{ in }\begin{cases}-x-y=10\\-x+2y=-14\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.