Question

Solve the following system of equations by graphing:

x - 3y = 9
y - 1 = 0

Answer 1

To solve the provided system of equations, each equation is converted into slope-intercept form and graphed. The solution is where the line y=(1/3)x-3 intersects the horizontal line y=1.

Step-by-step explanation:

The student is tasked with solving a system of equations consisting of x - 3y = 9 and y - 1 = 0 by graphing. To graph these equations, we must first rearrange each into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept. For the first equation, this gives us y = ⅓x - 3 and the second equation is already in slope-intercept form, y = 1. By creating a table of values or using the slope and intercept, we plot these two lines on a graph. The solution to the system will be the point where both lines intersect.

To graph the first equation, we start at the y-intercept (0, -3) and use the slope of ⅓ to rise 1 unit and run 3 units horizontally. We then plot the second equation as a horizontal line at y = 1. The intersection of these two lines represents the solution to the system of equations, which can be identified by observing the point on the graph where both lines meet.

Answer 2

The solution to the system of equations by graphing is found by plotting both equations on a coordinate plane. The first equation is converted to slope-intercept form and graphed, while the second equation is a horizontal line. Their point of intersection is the solution, which is (12, 1).

Step-by-step explanation:

To solve the system of equations by graphing, let's first rewrite the equation 'x - 3y = 9' in slope-intercept form, which is 'y = mx + b' where 'm' is the slope and 'b' is the y-intercept. We solve for 'y' and get 'y = rac{1}{3}x - 3'. Now, the second equation 'y - 1 = 0' simplifies to 'y = 1'. This is a horizontal line that crosses the y-axis at 1.

To graph 'y = rac{1}{3}x - 3', pick several values of 'x', substitute them into the equation, and solve for 'y' to find corresponding points. Plot these points on a coordinate plane and draw a line through them.

The slope is ¼, which means 'rise over run' is 1 for every 3 units of 'x'. To graph 'y = 1', draw a straight line parallel to the x-axis that crosses the y-axis at 1.

The solution to the system is the point where the two lines intersect. Since 'y = 1' is a horizontal line, it intersects 'y = rac{1}{3}x - 3' at the point where x satisfies ¼x - 3 = 1. Solving for 'x' gives 'x = 12'. Therefore, the solution to the system of equations is (12, 1).