Solve using elimination. 3/2y+z=3 and -y-2/3z=-2

Question

Please help me solve this using elimination.

3/2y+z=3

-y-2/3z=-2

 

Thanks!

Answer 1

Solve using elimination. 3/2y+z=3 and -y-2/3z=-2

Rewriting your eqns as,

(3/2)y + z = 3   ----------- (1)

-y - (2/3)z = -2   --------- (2)

multiply (2) by (3/2).

(3/2)y + z = 3 ------------- (3)

-(3/2)y - z = -3  ----------- (4)

Eqns (3) and (4) are the same equation, which means that they are coincident lines, which means that there is an infinite number of solutions, each solution being any point on either line/equation.

Answer 2

Assume question is based on: 3y/2+z=3 and -y-2z/3=-2.

Negate 2nd equation: y+2/3z=2 then multiply by 3/2: 3/2y+z=3, which is the 1st equation! So there are multiple solutions based on the relation between y and z. A graph of y plotted against z illustrates the dependency (y intercept is 2 and the z intercept is 3). There is no unique solution. The equation can be written 3y+2z=6.