Question

Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a system of linear equations that has one solution, no solution and infinitely many solutions? Solve each of the following systems by graphing. y = -x – 7 y = 4/3 x – 7 y = -3x – 5 y = x + 3 y = -2x + 5 y = 1/3 x – 2 3x + 2y = 2 x + 2y = -2 x + 3y = -9 2x – y = -4 x – 2y = 2 -x + 4y = -8 5x + y = -2 x + y = 2

Answer 1

75% I think x = -1, y = -3

Answer 2

Different ways to solve a system of linear equations:

• isolate one variable in one equation and replace it in the other equation
• multiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remains
• graph the equation and look at the intersection point

If you graph the system:

• there is only one solution if the lines intersects at only one point
• there is no solution if the lines don't intersect each other (they are parallel)
• there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)

Explanation:

1st system

y = -x – 7

y = 4/3 x – 7

solution: x= 0, y = 7

2nd system

y = -3x – 5

y = x + 3

solution: x = -2, y = 1

3rd system

y = -2x + 5

y = 1/3 x – 2

solution: x = 3, y = -1

4th system

3x + 2y = 2

x + 2y = -2

solution: x = 2, y = -2

5th system

x + 3y = -9

2x – y = -4

solution: x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution: x = -4, y = -3

7th system

5x + y = -2

x + y = 2

solution: x = -1, y = -3