Solve algebraically the simultaneous equations, giving your answers in terms of b : 3x+by=5, x-y=-2

First, I would label the two equations 1 and 2:(1) 3x+by=5(2)x-y=-2Next, multiply (2) by 3 and subtract this equation from (1) in order to cancel out the x terms: 3x+by=5-(3x-3y=-6)This results in the equation: by+3y=5+6 =11Next, factorise the LHS and divide in order to achieve an answer for y in terms of b:y(b+3)=11, so it follows that y=11/(b+3)Next, substitute this equation for y into (2) and rearrange this to get a solution for x:x-(11/b+3)=-2 adding (11/b+3 to both sides)x=(11/b+3)-2 (Multiplying to by (b+3) to get one fraction)x=(5-2b)/(b+3)