Question

20 points Without solving the systems, determine if there is 0, 1 or infinite solutions. Explain how you know.

Answer 1

Infinite Solutions.

Step-by-step explanation:

3x+2y=8 for x:

3x+2y=8

3x+2y+−2y=8+−2y(Add -2y to both sides)

3x=−2y+8 3x 3 = −2y+8 3 (Divide both sides by 3)

x= −2 3 y+ 8 3

Substitute −2/3y + 8/3 for x in 4.5x+3y=12:

4.5x+3y=12

4.5( −2/3y+ 8/3 )+3y=12

12=12(Simplify both sides of the equation)

12+−12=12+−12(Add -12 to both sides)

0=0

Infinitely many solutions.

Answer 2

Infinite Solutions.

Explanation:

3x+2y=8 for x:

3x+2y=8

3x+2y+−2y=8+−2y(Add -2y to both sides)

3x=−2y+8 3x 3 = −2y+8 3 (Divide both sides by 3)

x= −2 3 y+ 8 3

Substitute −2/3y + 8/3 for x in 4.5x+3y=12:

4.5x+3y=12

4.5( −2/3y+ 8/3 )+3y=12

12=12(Simplify both sides of the equation)

12+−12=12+−12(Add -12 to both sides)

0=0

Infinitely many solutions.