Step-by-step explanation:
Let x represent the first number, and y be the second number.
The first statement can be modeled as
[tex] {x}^{2} - {y}^{2} = 15[/tex]
The second statement can modeled as
[tex]2 {x}^{2} - {y}^{2} = 30[/tex]
If we multiply 2 both sides of the first equation,
[tex]2( {x}^{2} - {y}^{2} ) = 15 \times 2[/tex]
[tex]2 {x}^{2} - 2 {y}^{2} = 30[/tex]
Subsitue this for 30 in second equation,
[tex]2 {x}^{2} - {y}^{2} = 2 {x}^{2} - {2y}^{2} [/tex]
[tex] {y}^{2} = 0[/tex]
[tex]y = 0[/tex]
Subsitue this for y in either equation,
[tex] {x}^{2} = 15[/tex]So our answer is
plus or minus sqr root of 15, 0).
[tex](± \sqrt{15} ,0)[/tex]
[tex]x = \sqrt{15} [/tex]
or
[tex]x = - \sqrt{15} [/tex]
