Question

Solve the following system of equations graphically.

y=2x-3
x+y=3
What is the solution set?
O {(2, 1)]
O {(-2, -1)}
O {(1,2)
O {(-1,-2)]

Answer 1

Answer: (2, 1)

Explanation

The line y = 2x-3 goes through (0,-3) which is the y intercept.

This is because of the -3 at the end. The slope 2 = 2/1 means "go up 2, then right 1" so we move from (0,-3) to (1,-1)

Plot the points (0,-3) and (1,-1).

Draw a straight line through them to graph y = 2x-3.

The equation x+y = 3 solves to y = -x+3. Follow similar steps as done above to find two points on this line are (0,3) and (1,2)

See the graph shown below.

The two lines intersect at (2, 1) which is the solution. The x and y values of x = 2 and y = 1 make both original equations true.

Answer 2

To solve the system of equations graphically, plot both equations on graph paper, identify where they intersect and match this point with the provided choices to find the solution set.

Step-by-step explanation:

To solve the system of equations graphically, we need to plot both equations on the same set of axes and identify where they intersect. The first equation given in the question is y = 2x - 3. You would begin by creating a table with values of x to find y. Then plot these points on a graph and draw the line through them.

The second equation appears to have a typo, it should likely be 'x + y = 3' or a similar linear equation. Assuming 'x + y = 3' is the correct equation, solve for y (i.e., y = 3 - x), then create a table of values for x and corresponding values for y, plot the points, and draw the line.

The solution set is the point where the two lines intersect, which represents the values of x and y that satisfy both equations simultaneously. Match the intersection point with one of the choices provided to find the solution set.