Answers:
A) No solutions, elimination
B) Exactly one solution, substitution
Step-by-step explanation:
I'll be using elimination for this first one. I'm going to eliminate x by combining the equations.
First, let's multiply the top equation by 2.
2(-x + 5y = 8)
-2x + 10y = 16
Now, combine this equation with the bottom equation.
-2x + 10y = 16
<u>+ 2x - 10y = 7</u>
0 = 23
The result is false, so the first problem has no solution.
For the second problem, it would be better to use substitution because it would get pretty messy if we used elimination. I'm going to isolate x from the second equation.
-x + 2y = 0.6
Subtract 2y from both sides.
-x = -2y + 0.6
Divide both sides by -1 to make x positive.
x = 2y - 0.6
Now let's substitute x in the first equation.
0.5x + y = 0.3
0.5(2y - 0.6) + y = 0.3
y - 0.3 + y = 0.3
Combine like terms.
2y - 0.3 = 0.3
Add 0.3 to both sides.
2y = 0.6
Divide both sides by 2
y = 0.3
This problem has exactly one solution.
