Question

given $y = -9x + 8$, which equation would make a system with infinitely many solutions?
$\bigcirc$ $y = -9x - 7$
$\bigcirc$ $y = -4x + 3$
$\bigcirc$ $y = 2x - 2$
$\bigcirc$ $y = 8 - 9x$

Explanation:

Step1: Recall infinite solutions condition

A system of linear equations \( y = m_1x + b_1 \) and \( y = m_2x + b_2 \) has infinitely many solutions if \( m_1 = m_2 \) and \( b_1 = b_2 \) (they are the same line).

Step2: Analyze the given equation

The given equation is \( y = -9x + 8 \). We can rewrite \( y = 8 - 9x \) using the commutative property of addition: \( y=-9x + 8 \), which is identical to the given equation.
For the other options:

• \( y=-9x - 7 \): \( b=-7

eq8 \), so different line.

• \( y=-4x + 3 \): \( m=-4

eq - 9 \), different line.

• \( y = 2x-2 \): \( m = 2

eq-9 \), different line.

Answer:

\( y = 8 - 9x \) (the last option)