Respuesta :
[tex]y = {x}^{2} + 3x - 7 \\ and \\ 3x - y = 2[/tex]
From the second equation:
[tex]3x + 2 = y[/tex]
Substitute the value of y in the first equation:
[tex]3x + 2 = {x}^{2} + 3x - 7[/tex]
Rearrange the equation:
[tex]0 = {x}^{2} + 3x - 3x - 7 - 2 \\ \\ {x}^{2} - 9 = 0[/tex]
Using the "difference of two squares" approach:
[tex](x + 3)(x - 3) = 0[/tex]
Therefore the values of x can be
[tex]x + 3 = 0 \: or \: x - 3 = 0 \\ \\ x = - 3 \: or \: x = + 3[/tex]
Substitute either values of x in the second equation:
[tex]3( - 3) - y = 2 \: or \: 3(3) - y = 2 \\ \\ - 9 - y = 2 \: or \: 9 - y = 2[/tex]
y =-2 - 9 or y = 9 - 2
y = - 11 or y = 7
The answer is (-3, - 11) and (3, 7). The answer is D
From the second equation:
[tex]3x + 2 = y[/tex]
Substitute the value of y in the first equation:
[tex]3x + 2 = {x}^{2} + 3x - 7[/tex]
Rearrange the equation:
[tex]0 = {x}^{2} + 3x - 3x - 7 - 2 \\ \\ {x}^{2} - 9 = 0[/tex]
Using the "difference of two squares" approach:
[tex](x + 3)(x - 3) = 0[/tex]
Therefore the values of x can be
[tex]x + 3 = 0 \: or \: x - 3 = 0 \\ \\ x = - 3 \: or \: x = + 3[/tex]
Substitute either values of x in the second equation:
[tex]3( - 3) - y = 2 \: or \: 3(3) - y = 2 \\ \\ - 9 - y = 2 \: or \: 9 - y = 2[/tex]
y =-2 - 9 or y = 9 - 2
y = - 11 or y = 7
The answer is (-3, - 11) and (3, 7). The answer is D