Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a sy
stem 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
2 answers:
Answer:
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)
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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