Consider the system of simultaneous equations: | Equation | |---| | | | |

MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

Consider the system of simultaneous equations: | Equation | |---| |

3x - 2y = 12

| |

y = mx - 6

| (1) Find the gradient of each line. (2) Hence determine the value of

m

for which the simultaneous equations do *not* have a unique solution. Explain what is happening in this case. (3) For any other value of

m

, the system has a unique solution. Find this solution.