Answer:
[tex]x - 5y =12[/tex] and [tex]3x + 2y =-15[/tex]
Step-by-step explanation:
Given
See attachment
Required
Which options has the solution: [tex](x,y) = (-3,-3)[/tex]
[tex](a)[/tex] [tex]x - 5y =-12[/tex] and [tex]3x + 2y =-15[/tex]
Substitute [tex]x =-3[/tex] and [tex]y = -3[/tex] in [tex]x - 5y =-12[/tex] and [tex]3x + 2y =-15[/tex]
[tex]x - 5y =-12[/tex]
[tex]-3 - 5*-3 = -12[/tex]
[tex]-3 + 15 = -12[/tex]
[tex]12 \ne -12[/tex]
This is not a solution
[tex](b)[/tex] [tex]x - 5y =-12[/tex] and [tex]3x + 2y =15[/tex]
As shown in (a), (-3,-3) is not true for [tex]x - 5y =-12[/tex]
[tex](c)[/tex] [tex]x - 5y =12[/tex] and [tex]3x + 2y =-15[/tex]
Substitute [tex]x =-3[/tex] and [tex]y = -3[/tex] in [tex]x - 5y =12[/tex] and [tex]3x + 2y =-15[/tex]
[tex]x - 5y =12[/tex]
[tex]-3 - 5(-3) = 12[/tex]
[tex]-3 + 15 = 12[/tex]
[tex]12 = 12[/tex]
[tex]3x + 2y =-15[/tex]
[tex]3(-3) + 2(-3) = -15[/tex]
[tex]-9 - 6 = -15[/tex]
[tex]-15 = -15[/tex]
Hence,
(-3,-3) is true for [tex]x - 5y =12[/tex] and [tex]3x + 2y =-15[/tex]
