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

Different ways to solve a system of linear equations:

isolate one variable in one equation and replace it in the other equationmultiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remainsgraph 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 pointthere 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)

Step-by-step 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

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