Pertanyaan

Tentukan penyelesaian atau akar sistem persamaan berikut! 2 x 2 + 3 y 2 = 16 3 1 dan 4 x 2 − 3 y 2 = − 4 3 1

Tentukan penyelesaian atau akar sistem persamaan berikut!

$\frac{x ^{2}}{2} + \frac{y ^{2}}{3} = 16 \frac{1}{3}$ dan $\frac{x ^{2}}{4} - \frac{y ^{2}}{3} = - 4 \frac{1}{3}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

penyelesaiannya adalah dan .

penyelesaiannya adalah x equals 4 space atau space x equals negative 4

dan

y equals 5 space atau space y equals negative 5

Pembahasan

Diketahui sistem persamaan dan . Sistem persamaan di atas disederhanakan menjadi dan Menentukan Substitusi ke persamaan Substitusi ke persamaan Substitusi ke persamaan Jadi, penyelesaiannya adalah dan .

Diketahui sistem persamaan x squared over 2 plus y squared over 3 equals 16 1 third dan x squared over 4 minus y squared over 3 equals negative 4 1 third .

Sistem persamaan di atas disederhanakan menjadi

table attributes columnalign right center left columnspacing 0px end attributes row cell x squared over 2 plus y squared over 3 end cell equals cell 16 1 third end cell row cell left parenthesis x squared over 2 plus y squared over 3 end cell equals cell 49 over 3 right parenthesis times 6 end cell row cell 3 x squared plus 2 y squared end cell equals 98 end table dan table attributes columnalign right center left columnspacing 0px end attributes row cell x squared over 4 minus y squared over 3 end cell equals cell negative 4 1 third end cell row cell x squared over 4 minus y squared over 3 end cell equals cell negative 13 over 3 end cell row cell 3 x squared minus 4 y squared end cell equals cell negative 52 end cell end table

Menentukan x squared

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x squared plus 2 y squared end cell equals 98 row cell 3 x squared end cell equals cell negative 2 y squared plus 98 end cell row cell x squared end cell equals cell fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction end cell end table$

Substitusi $x squared equals fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction$ ke persamaan 3 x squared minus 4 y squared equals negative 52

$table attributes columnalign right center left columnspacing 0px end attributes row cell 3 x squared minus 4 y squared end cell equals cell negative 52 end cell row cell 3 left parenthesis fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction right parenthesis minus 4 y squared end cell equals cell negative 52 end cell row cell negative 2 y squared plus 98 minus 4 y squared end cell equals cell negative 52 end cell row cell negative 6 y squared end cell equals cell negative 52 minus 98 end cell row cell negative 6 y squared end cell equals cell negative 150 end cell row cell y squared end cell equals cell fraction numerator negative 150 over denominator negative 6 end fraction end cell row cell y squared end cell equals 25 row y equals cell 5 space atau space y equals negative 5 end cell end table$

Substitusi y equals 5 ke persamaan $x squared equals fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x squared end cell equals cell fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator negative 2 left parenthesis 5 right parenthesis squared plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator negative 2 left parenthesis 25 right parenthesis plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator negative 50 plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell 48 over 3 end cell row cell x squared end cell equals 16 row x equals cell 4 space atau space x equals negative 4 end cell end table$

Substitusi y equals negative 5 ke persamaan $x squared equals fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x squared end cell equals cell fraction numerator negative 2 y squared plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator negative 2 left parenthesis negative 5 right parenthesis squared plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator negative 2 left parenthesis 25 right parenthesis plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell fraction numerator negative 50 plus 98 over denominator 3 end fraction end cell row cell x squared end cell equals cell 48 over 3 end cell row cell x squared end cell equals 16 row x equals cell 4 space atau space x equals negative 4 end cell end table$

Jadi, penyelesaiannya adalah x equals 4 space atau space x equals negative 4 dan y equals 5 space atau space y equals negative 5 .