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
