Question

valerie and lily both wrote a linear equation to make up a system of equations. valerie graphed her equation and lily made a table of ordered pairs. which system of equation represents valerie and lilys lines? o 3x - y = 2 4x + 9y = 4 o 3x - y = 6 9x + 4y = 16 o x - 3y = 6 9x + 4y = 16 o x - 3y = 2 9x + 4y = 4

Explanation:

Step1: Find Lily's line equation

Use the two - point form $y - y_1=\frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$. Let $(x_1,y_1)=(-1,-9)$ and $(x_2,y_2)=(2,0)$. The slope $m=\frac{0 + 9}{2+1}=3$. Using the point - slope form with $(x_1,y_1)=(2,0)$, we have $y-0 = 3(x - 2)$, which simplifies to $y=3x - 6$ or $3x-y=6$.

Step2: Check Valerie's line

We can use the intercept form or test points on the graph. But since we have found Lily's line equation as $3x - y=6$, we can test the second equations of each option with the points from Lily's table. Substitute the points from Lily's table into the second equations of the options. For the equation $9x + 4y=16$. When $x = 2,y = 0$, $9\times2+4\times0=18
eq16$. When we consider the general form of linear equations and substitution of points from the table, we find that for Lily's line $3x - y=6$ and for Valerie's line (by elimination of other options) we can assume the second - equation in the system. The system of equations for Lily and Valerie is $3x - y=6$ and $9x + 4y=16$.

Answer:

$3x - y=6$
$9x + 4y=16$