# Solve system of equations and draw the graphs

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

#### Solution Preview

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 ...

#### Solution Summary

The expert solves a system of equations and draws the graph.