25) The answer is A, (2/5, 3/5).
26) The answer is A, the money per hour is 11 at the neighbor's yard and 8 at the retail store.
Explanation
25)
We can easily isolate x in the first equation:
x+y = 1
x+y-y=1-y
x = 1-y
Substitute this into the second equation:
10(1-y) + 5y = 7
Use the distributive property to multiply through:
10*1 - 10*y + 5y = 7
10 - 10y + 5y = 7
Combine like terms:
10 - 5y = 7
Cancel the 10 by subtracting from both sides:
10 - 5y - 10 = 7 - 10
-5y = -3
Divide both sides by -5:
-5y/-5 = -3/-5
y = 3/5
Substitute this back in to the first equation:
x + 3/5 = 1
x = 1 - 3/5 = 2/5
26)
Let x be the amount of money earned per hour at the neighbor's house and y be the amount of money earned per hour at the store. Our system of equations would be:
2x+3y = 49
x + 2y = 30
In the second equation, we can isolate x by subtracting 2y from both sides:
x + 2y - 2y = 30 - 2y
x = 30 - 2y
Substitute this into the first equation:
2(30 - 2y) + 3y = 49
Use the distributive property:
2*30 - 2*2y + 3y = 49
60 - 4y + 3y = 49
Combine like terms:
60 - y = 49
Subtract 60 from both sides:
60 - y - 60 = 49 - 60
-y = -11
Divide both sides by -1:
-y/-1 = -11/-1
y = 11
Substitute this back into the second equation:
x + 2*11 = 30
x + 22 = 30
Subtract both sides by 22:
x + 22 - 22 = 30 - 22
x = 8
