school
Acemy

Systems of Two Linear Equations in Two Variables

SAT Math· difficulty 5/5

For which value of kk does the system kx+(k+1)y=k+2kx + (k+1)y = k+2 and (k+1)x+ky=k+2(k+1)x + ky = k+2 have a unique solution that satisfies x=yx = y?

  • A

    k=−1k = -1

  • B

    All real kk except k=−12k = -\frac{1}{2}

    check_circle
  • C

    k=1k = 1

  • D

    k=0k = 0

Explanation

By symmetry, if x=yx = y, then (2k+1)x=k+2(2k+1)x = k+2 → x=k+22k+1x = \frac{k+2}{2k+1}, valid when 2k+1≠02k + 1 \neq 0, i.e., k≠−12k \neq -\frac{1}{2}.

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forwardPredict my AP score

Related questions

auto_awesomeAll Toolsquestion_answerHomework Q&Amenu_bookAP & SAT PreptimelineLearn Mode