Answer:
Step-by-step explanation:
The given question is
Does the following system have One Solution, No Solution, or Infinite Solutions.
[tex]y = 4x + 8\\y = -5x + 3[/tex]
To solve this system, we just need to multiply the first equation by -1, and then sum those equations.
[tex]-y = -4x - 8\\y = -5x + 3[/tex]
[tex]0=-9x-5\\5=-9x\\x=-\frac{5}{9}[/tex]
Then, we use this value to find the other one
[tex]y=4x+8\\y=4(-\frac{5}{9} )+8\\y=-\frac{20}{9}+8\\y =\frac{-20+72}{9} \\y=\frac{52}{9}[/tex]
As you can observe, the system of equations have a unique solution.
Therefore, the answer is one solution.
