Solve system of equations and draw the graphs
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Question 1 - Draw the graphs of 2x-y-1 = 0 and 2x + y = 9; Write down the co-ordinates of the point of intersection of the two lines.
Question 2 - Solve graphically x + y + 2 = 0 and 3x - 4y = 5. Write down the co-ordinates of the point of intersection of the two lines.
Question 3 - Solve graphically x = 4 and 3x - 2y = 10. Write down the co-ordinates of the point of intersection of the two lines.
Question 4 - Show graphically that the system of linear equations 2x+4y=10 and 3x + 6y = 12 has no solution. Explain why.
Question 5 - Solve graphically: 3x + y + 1 = 0 and 2x - 3y + 8 = 0. Write down the co-ordinates of the point of intersection of the two lines.
Question 6 - Solve graphically y = 2x - 6 and y = -2x + 10. Write down the co-ordinates of the point of intersection of the two lines.
Question 7 - Solve graphically: 3y = 5 - x and 2x = y + 3. Write down the co-ordinates of the point of intersection of the two lines.
Question 8 - Solve graphically: x + y = -1 and y - 2x = -4. Write down the co-ordinates of the point of intersection of the two lines.
3. Solve the system of equations
x + 3y = 32
-3x + 2y = 8
4. Solve the system of equations
x + y = 6
x - y = -7
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Solution Summary
The expert solves a system of equations and draws the graph.
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MAT101 - Module 2 (part II) - Case Assignment
Example Question and Solution
Solve graphically x - 2y = 1 and x + y = 4, and write down the co-ordinates of the point of intersection of the two lines.
Use grid below. When you click on the arrows you can move and/or rotate them to the correct position.
Plot only 3 points per line.
Answer:
x - 2y = 1
2y = x - 1
y=(x-1)/2
X -3 3 5
y -2 1 2
See RED arrow denoting the linear function and a positive slope
x + y = 4
y = 4 - x
X 0 1 4
y 4 3 0
See BLUE arrow denoting the linear function and a negative slope
The intersection of the two lines has the value of (3,1) which solves BOTH equations.
5
4
3
2
1
-5
-4 -3 -2 -1 0 1 2 3 4
-1
-2
-3
-4
Following the example above, solve the following EIGHT (8) questions, moving the arrows to and in the table.
Question 1 - Draw the graphs of 2x-y-1 = 0 and 2x + y = 9; Write down the co-ordinates of the point of intersection of the two lines.
Answer:
2x-y-1 = 0
y = 2x - 1
x -1 2 1
y -2 3 1
See RED arrow denoting the linear function and a positive slope
2x + y = 9
y = 9 - 2x
X 0 3 4
y 9 3 1
See BLUE arrow denoting the linear function and a negative slope
5
4
3
2
1
-5
-4 -3 -2 -1 0 1 2 3 4
-1
-2
-3
-4
The intersection of the two lines has the value of (4, 2.5) which solves BOTH equations.
Question 2 - Solve graphically x + y + 2 = 0 and 3x - 4y = 5. Write ...
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