Final answer:
In this case, the linear system has one solution: (2.5, 0)
The answer is option ⇒b.
Step-by-step explanation:
To find the solution to the given system of equations, we substitute the value of y from the first equation into the second equation.
The first equation is y = 2x - 5.
In the second equation, -8x - 4y = -20, we replace y with 2x - 5:
-8x - 4(2x - 5) = -20.
Simplifying this equation, we distribute the -4:
-8x - 8x + 20 = -20.
Combining like terms, we have:
-16x + 20 = -20.
To isolate the variable x, we subtract 20 from both sides of the equation:
-16x = -40.
Dividing both sides by -16, we get:
x = -40 / -16.
Simplifying, we have:
x = 2.5.
Now that we have found the value of x, we can substitute it back into the first equation to find the value of y.
Using the first equation y = 2x - 5, we replace x with 2.5:
y = 2(2.5) - 5.
Simplifying, we have:
y = 5 - 5.
Further simplifying, we find:
y = 0.
Therefore, the solution to the given system of equations is x = 2.5 and y = 0.
The answer is option ⇒b) one solution: (2.5, 0)
Your question is incomplete, but most probably the full question was:
How many solutions does this linear system have?
y = 2x – 5
–8x – 4y = –20
Options:
A- one solution: (–2.5, 0)
B- one solution: (2.5, 0)
C- no solution
D- infinite number of solutions