Question

how many solutions does this linear system have?
y = 2x − 5
−8x − 4y = −20
one solution: (−2.5, 0)
one solution: (2.5, 0)
no solution
infinite number of solutions

Explanation:

Step1: Substitute \( y = 2x - 5 \) into the second equation

Substitute \( y \) in \( -8x - 4y = -20 \) with \( 2x - 5 \). So we get \( -8x - 4(2x - 5) = -20 \).

Step2: Simplify the equation

First, expand the bracket: \( -8x - 8x + 20 = -20 \). Then combine like terms: \( -16x + 20 = -20 \). Subtract 20 from both sides: \( -16x = -40 \). Divide both sides by -16: \( x=\frac{-40}{-16}=2.5 \).

Step3: Find the value of \( y \)

Substitute \( x = 2.5 \) into \( y = 2x - 5 \). So \( y = 2\times2.5 - 5 = 5 - 5 = 0 \). So the solution is \( (2.5, 0) \), which means there is one solution.

Answer:

one solution: (2.5, 0)