Consider the equation 6x+3y=9 Which equation, when graphed with the given equation, will form a system wit nfinitely many solutions? y+2x=3 y+2x=9 y=2x+3 y=-2x+9

To determine which equation, when graphed with the given equation $6x+3y=9$, will form a system with infinitely many solutions, we need to find an equation that is equivalent to the given equation.<br /><br />Let's analyze each option:<br /><br />1. $y+2x=3$: This equation is not equivalent to the given equation $6x+3y=9$. Therefore, it will not form a system with infinitely many solutions.<br /><br />2. $y+2x=9$: This equation is also not equivalent to the given equation $6x+3y=9$. Therefore, it will not form a system with infinitely many solutions.<br /><br />3. $y=2x+3$: This equation is equivalent to the given equation $6x+3y=9$. To verify, we can rearrange the given equation to solve for $y$:<br />$6x+3y=9$<br />$3y=9-6x$<br />$y=3-\frac{6}{3}x$<br />$y=3-2x$<br />Therefore, the given equation $6x+3y=9$ is equivalent to $y=2x+3$. When graphed together, they will form a system with infinitely many solutions.<br /><br />4. $y=-2x+9$: This equation is not equivalent to the given equation $6x+3y=9$. Therefore, it will not form a system with infinitely many solutions.<br /><br />Based on the analysis, the equation that, when graphed with the given equation $6x+3y=9$, will form a system with infinitely many solutions is $y=2x+3$.