Question

Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
4x – 6y = 30
3x – 5y = 24 (Points : 20)

Answer 1

4x – 6y = 30 ---eqn(I)
3x – 5y = 24 ---eqn(II)

multiply eqn(I) with 3 and eqn(II) with 4

3(4x – 6y = 30)

12x-18y=90 ----eqn(III)

4(3x – 5y = 24)

12x-20y=96 -----eqn(IV)

subtract eqn(IV) from eqn(III)

12x-18y=90
-(12x-20y=96)

---------------
2y= -6

so y=-3

put this value in any of the given eqns and get value of x

4x – 6y = 30
4x-6(-3)=30
4x+18=30
3x=12
x=3

so the solution set is (3,-3)