Resposta:

[tex]\textsf{Leia abaixo}[/tex]

Explicação passo a passo:

[tex]\begin{cases}\mathsf{3x^2 - 4y^2 = 11\rightarrow(I)}\\\mathsf{2x^2 + 4y^2 = 34\rightarrow(II)}\end{cases}[/tex]

[tex]\textsf{Somando (I) e (II)}[/tex]

[tex]\mathsf{5x^2 = 45}[/tex]

[tex]\mathsf{x^2 = 9}[/tex]

[tex]\mathsf{x = \pm\:\sqrt{9}}[/tex]

[tex]\boxed{\boxed{\mathsf{x = \pm\:3}}}[/tex]

[tex]\mathsf{3(3^2) - 4y^2 = 11}[/tex]

[tex]\mathsf{4y^2 = 27 - 11}[/tex]

[tex]\mathsf{4y^2 = 16}[/tex]

[tex]\mathsf{y^2 = 4}[/tex]

[tex]\mathsf{y = \pm\:\sqrt{4}}[/tex]

[tex]\boxed{\boxed{\mathsf{y = \pm\:2}}}[/tex]