Pertanyaan

Tentukan penyelesaian atau akar sistem persamaan berikut! 2 x 2 + 4 5 y 2 = 25 4 3 dan 3 4 y 2 − 2 1 x 2 = − 23 6 1

Tentukan penyelesaian atau akar sistem persamaan berikut!

$\frac{x ^{2}}{2} + \frac{5 y ^{2}}{4} = 25 \frac{3}{4}$ dan $\frac{4}{3} y^{2} - \frac{1}{2} x^{2} = - 23 \frac{1}{6}$

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

penyelesaiannya adalah dan .

penyelesaiannya adalah x equals 7 space atau space x equals negative 7

dan

y equals 1 space atau space y equals negative 1

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 $x squared over 2 plus fraction numerator 5 y squared over denominator 4 end fraction equals 25 3 over 4$ dan 4 over 3 y squared minus 1 half x squared equals negative 23 1 over 6 .

Sistem persamaan di atas disederhanakan menjadi

$table attributes columnalign right center left columnspacing 0px end attributes row cell x squared over 2 plus fraction numerator 5 y squared over denominator 4 end fraction end cell equals cell 25 3 over 4 end cell row cell left parenthesis x squared over 2 plus fraction numerator 5 y squared over denominator 4 end fraction end cell equals cell 103 over 4 right parenthesis times 4 end cell row cell 2 x squared plus 5 y squared end cell equals 103 end table$ dan

Menentukan x squared

$table attributes columnalign right center left columnspacing 0px end attributes row cell 16 y squared minus 6 x squared end cell equals cell negative 278 end cell row cell 16 y squared plus 278 end cell equals cell 6 x squared end cell row cell fraction numerator 16 y squared plus 278 over denominator 6 end fraction end cell equals cell x squared end cell end table$

Substitusi $x squared equals fraction numerator 16 y squared plus 278 over denominator 6 end fraction$ ke persamaan 2 x squared plus 5 y squared equals 103

$table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x squared plus 5 y squared end cell equals 103 row cell 2 left parenthesis fraction numerator 16 y squared plus 278 over denominator 6 end fraction right parenthesis plus 5 y squared end cell equals 103 row cell fraction numerator 32 y squared plus 556 over denominator 6 end fraction plus fraction numerator 30 y squared over denominator 6 end fraction end cell equals 103 row cell fraction numerator 62 y squared plus 556 over denominator 6 end fraction end cell equals 103 row cell 62 y squared plus 556 end cell equals 618 row cell 62 y squared end cell equals cell 618 minus 556 end cell row cell 62 y squared end cell equals 62 row cell y squared end cell equals 1 row y equals cell 1 space atau space y equals negative 1 end cell row blank blank blank end table$

Substitusi y equals 1 ke persamaan $x squared equals fraction numerator 16 y squared plus 278 over denominator 6 end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x squared end cell equals cell fraction numerator 16 left parenthesis 1 right parenthesis squared plus 278 over denominator 6 end fraction end cell row cell x squared end cell equals cell fraction numerator 16 left parenthesis 1 right parenthesis plus 278 over denominator 6 end fraction end cell row cell x squared end cell equals cell 294 over 6 end cell row cell x squared end cell equals 49 row x equals cell 7 space atau space x equals negative 7 end cell end table$

Substitusi y equals negative 1 ke persamaan $x squared equals fraction numerator 16 y squared plus 278 over denominator 6 end fraction$

$table attributes columnalign right center left columnspacing 0px end attributes row cell x squared end cell equals cell fraction numerator 16 left parenthesis negative 1 right parenthesis squared plus 278 over denominator 6 end fraction end cell row cell x squared end cell equals cell fraction numerator 16 left parenthesis 1 right parenthesis plus 278 over denominator 6 end fraction end cell row cell x squared end cell equals cell 294 over 6 end cell row cell x squared end cell equals 49 row x equals cell 7 space atau space x equals negative 7 end cell end table$

Jadi, penyelesaiannya adalah x equals 7 space atau space x equals negative 7 dan y equals 1 space atau space y equals negative 1 .