for what values of theta does these simultaneous equations hold true?

(costheta)x - (sintheta)y = 2

(sintheta)x + (costheta)y = 1

So

(costheta)x= 2+ (sintheta)y

x= (2+ sintheta y)/costheta

And

(sintheta)x = 1- (costheta)y

x = (1- (costheta)y)/(sintheta)

(2+ sintheta y)/costheta= (1- (costheta)y)/(sintheta)

2sintheta+sin^2 theta y=costheta-cos^2theta y

sin^2 theta y +cos^2theta y=costheta-2sintheta

y=costheta-2sintheta

(costheta)x= 2+ (sintheta)(costheta-2sintheta)

x= (2+ (sintheta)(costheta-2sintheta))/(costheta)

x= (2+ sintheta costheta-2sin^2theta))/(costheta)

x= ( sintheta costheta-2cos^2theta))/(costheta)

x= ( sintheta-2costheta)

remedy for y interior the 2nd equation: x - y + 2 = 0 x + 2 = y Now equate the two equations: x + 2 = x² - x - 6 x² - 2x - 8 = 0 (x + 2)(x - 4) = 0 consequently, we've that: x = -2 or x = 4 which yields (via substituting into between the equations above and fixing for y) that y = 0 or y = 6 respectively. Or the answer could be written like this (-2, 0) and (4, 6). desire this helps!