Question

For each of the following system of linear equations, state the number of solutions without solving the system. a) -x+3y=9, -4x+12y=12 b) 2x-y-4=0,6x=3y+12

Answer 1

a) ONE SOLUTION

b) INFINITE SYSTEM OF SOLUTIONS

Explanation:

Given the system of equations;

a) x+3y=9

-4x+12y=12

This equation is a linear simultaneous equation with 2 equations and two unknown values. When the number of equations given is equal to the number of unknown variables, this means that the solution sets of the equations are unique and real and will provide us with just one solution.

b) For the system of linear equation

2x-y-4=0 .... *3

6x=3y+12 ... *1

First lets multiply equation 1 by 3, om multiplying by 3 we will have;

6x-3y-12 = 0

6x-3y = 0+12

6x-3y = 12

Rearranging equation 2 will give;

6x - 3y = 12

It is seen that both equation ate the same. This means that what we have is one equation with two unknowns. For a system of equation with one equation and two unknowns, there will be infinite number of solutions after solving the equation. Hence, the number of solutions for this system of equation is INFINITE