Fine the solution set of each system of linear equations or inequalities below by graphing. Show all work under the graph of each system.
1. x + y = 3
2x - 2y = 6
we cannot show graphs in this forum
make a table of values for each equation
plot the points for each line, and draw the lines through the points
(they should intersect at (3,0) )
To find the solution set of the system of linear equations by graphing, we will first graph each equation on the same coordinate plane. Then we will identify the point where the lines intersect, which represents the solution to the system of equations.
1. Start by graphing the equation x + y = 3:
- To graph this equation, we need to find at least two points on the line.
- For instance, when x = 0, we have 0 + y = 3, which gives y = 3. So one point is (0, 3).
- When y = 0, we have x + 0 = 3, which gives x = 3. Another point is (3, 0).
- Plot these two points and draw a line passing through them.
2. Now let's graph the equation 2x - 2y = 6:
- Similarly, find two points that satisfy this equation.
- When x = 0, we have 2(0) - 2y = 6, which gives -2y = 6 and y = -3. One point is (0, -3).
- When y = 0, we have 2x - 2(0) = 6, which gives 2x = 6 and x = 3. Another point is (3, 0).
- Plot these two points and draw a line through them.
3. Next, look for the point where the two lines intersect. This point is the solution to the system of equations.
- In this case, the lines intersect at the point (1, 2).
4. Finally, write the solution set of the system of equations:
- The solution set is {(1, 2)}.
Below the graph, you would show the work you did in finding the coordinates of the intersection point (1, 2) by solving the system of equations algebraically.