Question

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

Explanation:

Step1: Recall infinite solutions condition

A system of linear equations has infinitely many solutions if the equations are identical (same slope and same y - intercept). The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

For the given equation $y=-4x + 3$, the slope $m=-4$ and the y - intercept $b = 3$.

Step2: Analyze each option

• Option 1: For $y = 2x-7$, the slope $m = 2$ and y - intercept $b=-7$. Since the slope is different from - 4, this line is not the same as $y=-4x + 3$.
• Option 2: For $y=3 - 4x$, we can rewrite it in slope - intercept form as $y=-4x + 3$. The slope $m=-4$ and the y - intercept $b = 3$, which is the same as the given equation $y=-4x + 3$.
• Option 3: For $y = 2x-2$, the slope $m = 2$ and y - intercept $b=-2$. Since the slope is different from - 4, this line is not the same as $y=-4x + 3$.
• Option 4: For $y=2x + 8$, the slope $m = 2$ and y - intercept $b = 8$. Since the slope is different from - 4, this line is not the same as $y=-4x + 3$.

Answer:

B. $y = 3-4x$ (Here we assume the second option is labeled as B, following the order of the options in the problem. If the original problem has different labels, adjust accordingly. But based on the options provided, the equation $y = 3-4x$ is the one that makes the system have infinitely many solutions as it is equivalent to $y=-4x + 3$)