Question

What does it mean unique solution in simultaneous equations

Answer 1

Condition for Unique Solution to Linear Equations. A system of linear equations ax + by + c = 0 and dx + ey + g = 0 will have a unique solution if the two lines represented by the equations ax + by + c = 0 and dx + ey + g = 0 intersect at a point. i.e., if the two lines are neither parallel nor coincident.

Answer 2

ANSWER

$Given equations are x+(a </p><p>2</p><p> −3a+3)y=a </p><p>2</p><p> and x+y=1</p><p>To have unique equations, </p><p>a </p><p>2</p><p> </p><p> </p><p>a </p><p>1</p><p> </p><p> </p><p> </p><p> </p><p></p><p> </p><p> = </p><p>b2</p><p>b1</p><p> </p><p> </p><p>where, a </p><p>1</p><p> </p><p> and a </p><p>2</p><p> </p><p> are X-coefficients</p><p>b </p><p>1</p><p> </p><p> and b </p><p>2</p><p> </p><p> are Y-coefficients of the given equations. </p><p>Therefore, </p><p>1</p><p>1</p><p> </p><p> </p><p></p><p> </p><p> =a </p><p>2</p><p> −3a+3</p><p>a </p><p>2</p><p> −3a+2 </p><p></p><p> </p><p> =0</p><p>a </p><p></p><p> </p><p> =2 or a </p><p></p><p> </p><p> =1$

The values of a∈R−{1,2} for the unique solutions.