Speed< > to change
Math · 04 · Algebra · Free

Linear Algebra I

Notes

Key points

  • Distribute, collect x-terms on one side, constants on the other, then divide.
  • Fractions? Multiply every term by the LCD before anything else.
  • No solution: same xx-coefficient, different constants, e.g. 3x+2=3x+53x+2=3x+5.
  • Infinitely many: both sides identical after simplifying, e.g. 2(x+1)=2x+22(x+1)=2x+2.
  • One solution: the xx-coefficients differ.
  • Asked for 4x+24x+2, not xx? Scale the equation and skip solving.

Formulas

One solutionax+b=cx+d, a≠c ⇒ x=d−ba−cax+b=cx+d,\ a\neq c\ \Rightarrow\ x=\dfrac{d-b}{a-c}
No solutiona=c, b≠da=c,\ b\neq dVariables cancel, false statement left
Infinitely many solutionsa=c, b=da=c,\ b=dVariables cancel, true statement left
Literal equationv=u+at ⇒ t=v−uav=u+at\ \Rightarrow\ t=\dfrac{v-u}{a}Isolate the target letter like any variable

Common traps

  • Distributing a negative: −2(x−3)=−2x+6-2(x-3)=-2x+6, not −2x−6-2x-6.
  • Multiplying only some terms by the LCD.
  • Solving for xx when the question asks for an expression like 3x−13x-1.

SAT tip

“No solution for what value of k?” Match the x-coefficients, then check the constants differ.

Test yourself

10 official SAT questions on Linear Algebra I, easiest first.

    Next lesson05 · Linear Algebra II