Full solution

Q. How do you graph

24x+32y=264

and

x+y=9

Convert to slope-intercept form: Start with the first equation $24x + 32y = 264$ . To graph this equation, we need to write it in slope-intercept form ( $y = mx + b$ ), where $m$ is the slope and $b$ is the y-intercept.
Plot first equation on graph: Convert $24x + 32y = 264$ to slope-intercept form. $\newline$ Divide the entire equation by $32$ to isolate $y$ . $\newline$ $y = -\frac{24}{32} x + \frac{264}{32}$ $\newline$ Simplify the fractions. $\newline$ $y = -\frac{3}{4} x + \frac{33}{4}$ $\newline$ Now we have the slope $(-\frac{3}{4})$ and the y-intercept $(\frac{33}{4})$ .
Find second point for first equation: Plot the $y$ -intercept of the first equation on the graph. $\newline$ The $y$ -intercept is the point where the line crosses the $y$ -axis, which is at $(0, \frac{33}{4})$ .
Draw line for first equation: Use the slope to find another point. $\newline$ From the y-intercept $(0, \frac{33}{4})$ , move down $3$ units (since the slope is negative) and to the right $4$ units (the denominator of the slope). This gives us a second point on the line.
Graph second equation: Draw the line through the two points for the first equation. $\newline$ This line represents all the solutions to the equation $24x + 32y = 264$ .
Plot second equation on graph: Now, graph the second equation $x + y = 9$ . To graph this, we can also write it in slope-intercept form. Subtract $x$ from both sides to isolate $y$ . $y = -x + 9$ Now we have the slope $(-1)$ and the y-intercept $(9)$ .
Find second point for second equation: Plot the y-intercept of the second equation on the graph. $\newline$ The y-intercept is the point where the line crosses the y-axis, which is at $(0, 9)$ .
Draw line for second equation: Use the slope to find another point for the second equation. $\newline$ From the y-intercept $(0, 9)$ , move down $1$ unit and to the right $1$ unit (since the slope is $-1$ ). This gives us a second point on the line.
Draw line for second equation: Use the slope to find another point for the second equation. $\newline$ From the y-intercept $(0, 9)$ , move down $1$ unit and to the right $1$ unit (since the slope is $-1$ ). This gives us a second point on the line.Draw the line through the two points for the second equation. $\newline$ This line represents all the solutions to the equation $x + y = 9$ .