Answer:
Option 2 - One solution: (2.5, 0)
Step-by-step explanation:
Given : Two linear equation -
Equation 1 - [tex]y = 2x - 5[/tex]
Equation 2 - [tex]-8x - 4y = -20[/tex]
To find : How many solutions does this linear system have?
Solution :
We solve the given equations,
Substitute the value of y from equation 1 in equation 2
[tex]-8x - 4y = -20[/tex]
[tex]-8x - 4(2x-5) = -20[/tex]
[tex]-8x - 8x+20 = -20[/tex]
[tex]-16x=-40[/tex]
[tex]x=\frac{40}{16}[/tex]
[tex]x=2.5[/tex]
Now, put value of x in equation 1
[tex]y = 2x - 5[/tex]
[tex]y = 2(2.5) - 5[/tex]
[tex]y = 5 - 5[/tex]
[tex]y = 0[/tex]
There is one solution (x,y) = (2.5, 0)
Option 2 is correct.
