Question

4x+4y=32

3x+24=3y

Determine whether the system has one solution, no solution, or infinitely many solutions. Explain

Answer 1

The given system of equations 4x + 4y = 32 and 3x + 24 = 3y has only one solution

Solution:

Given, system of equations are:

4x + 4y = 32 ---- eqn (1)

3x + 24 = 3y ----- eqn (2)

We have to determine whether the system has one solution, no solution, or infinitely many solutions.

Now let us solve the given system of equations to determine.

Now, eqn (1) can be written as,

4(x + y) = 32

x + y = 8

x = 8 – y

So, substitute "x" value in eqn (2) to get the value of "y"

3(8 – y) + 24 = 3y

24 – 3y + 24 = 3y

48 = 3y + 3y

y = 8

Then, x = 8 – 8 = 0

Hence we got x = 0 and y = 8

Hence, the given system of equations has only one solution (x, y) = (0, 8)