MATH SOLVE

5 months ago

Q:
# *Please Help!* (Will give brainliest!)Classify each system of equations as having a single solution, no solution, or infinite solutions.

Accepted Solution

A:

put them all in y = mx + b form.....we need to compare the slopes and the y int's

y = 5 - 2x....rearrange...y = -2x + 5....slope = -2, y int = 5

4x + 2y = 10....2y = -4x + 10....y = -2x + 5....slope = -2, y int = 5

same slope, same y int.....infinite solutions

x = 26 - 3y....x - 26 = -3y......-1/3x + 26/3 = y....y = -1/3x + 26/3...slope = -1/3, y int = 26/3

2x + 6y = 22.....6y = -2x + 22....y = -1/3x + 11/3.....slope = -1/3, y int = 11/3.......same slope, different y int....means no solution

5x + 4y = 6......4y = -5x + 6.....y = -5/4x + 3/2....slope = -5/4, y int = 3/2

10x - 2y = 7....-2y = -10x + 7....y = 5x - 7/2....slope = 5 and y int = -7/2

different slopes, different y int....one solution

x + 2y = 3...2y = -x + 3....y = -1/2x + 3/2.....slope = -1/2, y int = 3/2

4x + 8y = 15....8y = -4x + 15.....y = -1/2x + 15/8.....slope = -1/2, y int = 15/8.......same slope, different y int.....no solution

3x + 4y = 17....4y = -3x + 17......y = -3/4x + 17/4.....slope = -3/4, y int = 17/4

-6x = 10y - 39...-6x + 39 = 10y....y = - 3/5x + 39/10...slope = -3/5, y int = 39/10....different slopes, different y int....one solution

x + 5y = 24....5y = -x + 24....y = -1/5x + 24/5....slope = -1/5, y int = 24/5

5x = 12 - y.....5x - 12 = -y.....y = -5x + 12...slope = -5, y int = 12

different slopes, different y int.....one solution

y = 5 - 2x....rearrange...y = -2x + 5....slope = -2, y int = 5

4x + 2y = 10....2y = -4x + 10....y = -2x + 5....slope = -2, y int = 5

same slope, same y int.....infinite solutions

x = 26 - 3y....x - 26 = -3y......-1/3x + 26/3 = y....y = -1/3x + 26/3...slope = -1/3, y int = 26/3

2x + 6y = 22.....6y = -2x + 22....y = -1/3x + 11/3.....slope = -1/3, y int = 11/3.......same slope, different y int....means no solution

5x + 4y = 6......4y = -5x + 6.....y = -5/4x + 3/2....slope = -5/4, y int = 3/2

10x - 2y = 7....-2y = -10x + 7....y = 5x - 7/2....slope = 5 and y int = -7/2

different slopes, different y int....one solution

x + 2y = 3...2y = -x + 3....y = -1/2x + 3/2.....slope = -1/2, y int = 3/2

4x + 8y = 15....8y = -4x + 15.....y = -1/2x + 15/8.....slope = -1/2, y int = 15/8.......same slope, different y int.....no solution

3x + 4y = 17....4y = -3x + 17......y = -3/4x + 17/4.....slope = -3/4, y int = 17/4

-6x = 10y - 39...-6x + 39 = 10y....y = - 3/5x + 39/10...slope = -3/5, y int = 39/10....different slopes, different y int....one solution

x + 5y = 24....5y = -x + 24....y = -1/5x + 24/5....slope = -1/5, y int = 24/5

5x = 12 - y.....5x - 12 = -y.....y = -5x + 12...slope = -5, y int = 12

different slopes, different y int.....one solution