Consider the system of equations. y=-2x+4 3y+x=-3 Which statement is true of this system of equations? Both equations are in slope-intercept form. The first equation converted to slope-intercept form is y+2x=4 The second equation converted to slope-intercept form is y=-(1)/(3)x-1 Neither equation is in slope-intercept form.

To determine which statement is true about the system of equations, we need to analyze each equation and see if it is in slope-intercept form.<br /><br />The slope-intercept form of a linear equation is given by:<br />$y = mx + b$<br />where $m$ is the slope and $b$ is the y-intercept.<br /><br />Let's analyze each equation:<br /><br />1. $y = -2x + 4$<br /> This equation is already in slope-intercept form, with a slope of $-2$ and a y-intercept of $4$.<br /><br />2. $3y + x = -3$<br /> To convert this equation to slope-intercept form, we need to isolate $y$:<br /> $3y = -x - 3$<br /> $y = -\frac{1}{3}x - 1$<br /><br />Now let's evaluate the statements:<br /><br />A. Both equations are in slope-intercept form.<br /> This statement is false because the second equation is not initially in slope-intercept form.<br /><br />B. The first equation converted to slope-intercept form is $y + 2x = 4$.<br /> This statement is false because the correct conversion of the first equation to slope-intercept form is $y = -2x + 4$.<br /><br />C. The second equation converted to slope-intercept form is $y = -\frac{1}{3}x - 1$.<br /> This statement is true because we derived this form from the second equation.<br /><br />D. Neither equation is in slope-intercept form.<br /> This statement is false because the first equation is already in slope-intercept form.<br /><br />Therefore, the correct answer is:<br />C. The second equation converted to slope-intercept form is $y = -\frac{1}{3}x - 1$.