Under what circumstances does the system of equations Qx+Ry=S and Y=Tx+S have infinitely many solutions?

Question

Mathematics

Davon Harmon

6 September, 03:14

Under what circumstances does the system of equations Qx+Ry=S and Y=Tx+S have infinitely many solutions?

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Dakota Combs · Answer 1

From these - Tx+y=S. If - T=Q/R, then y=-Qx/R+S, so Ry=-Qx+RS, Qx+Ry=RS=S.

If R is not equal to 1, or S is non-zero, the equations are inconsistent, so there would be no solutions.

If R=1 there are an infinite number of solutions given by Qx+y=S, or y=S-Qx or y=S+Tx.

If S=0, Qx+Ry=0 or y=-Qx/R or y=Tx.