Answer:
No Solution:
Top Middle
Top Right
One Solution:
Top Left
Bottom Left
Bottom Middle
Infinite:
Bottom Right
Explanation:
I will show one of each as an example for you to use. Here is the first one, it has one solution because it has a value for both x and y.
Let's solve your system by substitution.
−8x−10y=24;6x+5y=2
Solve−8x−10y=24 for x:
−8x−10y=24
−8x−10y+10y=24+10y(Add 10y to both sides)
−8x=10y+24
−8x−8=10y+24−8(Divide both sides by -8)
x=−54y−3
Substitute−54y−3 for x in6x+5y=2:
6x+5y=2
6(−54y−3)+5y=2
−52y−18=2(Simplify both sides of the equation)
−52y−18+18=2+18(Add 18 to both sides)
−52y=20
−52y−52=20−52(Divide both sides by (-5)/2)
y=−8
Substitute−8 for y in x=−54y−3:
x=−54y−3
x=−54(−8)−3
x=7(Simplify both sides of the equation)
Answer:
x=7 and y=−8
Next, a no solution problem. We will use the second system of equations.
Rewrite equations:
−x+y=3;−3x+3y=4
Solve−x+y=3 for y:
−x+y=3
−x+y+x=3+x(Add x to both sides)
y=x+3
Substitute x+3 for y in−3x+3y=4:
−3x+3y=4
−3x+3(x+3)=4
9=4(Simplify both sides of the equation)
9+−9=4+−9(Add -9 to both sides)
0=−5
This is not possible. Thus, there is no solution.
Lastly, a infinite solution problem. We will use the last system.
Solve 2x+8y=6 for x:
2x+8y=6
2x+8y+−8y=6+−8y(Add -8y to both sides)
2x=−8y+6
2x2=−8y+62(Divide both sides by 2)
x=−4y+3
Substitute −4y+3 for x in−5x−20y=−15:
−5x−20y=−15
−5(−4y+3)−20y=−15
−15=−15(Simplify both sides of the equation)
−15+15=−15+15(Add 15 to both sides)
0=0
It is equal, meaning that there are infinite solutions.
combine your like terms and you have your original expression of 
