Irina has 10 coins, all nickels and dimes, worth a total of $0.70. this is shown by the system of linear equations, x + y = 10 and 0.05x + 0.1y = 0.7, on the graph. how many nickels does she have? 4 6 7 10

X= # of dimes
y= # of nickels

QUANTITY EQUATION
x + y = 10

COST EQUATION
0.05x + 0.1y = 0.7

Solve for either variable in quantity equation and substitute answer in cost equation to solve.

x + y= 10
subtract both sides by y
x= 10 - y

0.05x + 0.1y= 0.7
0.05(10-y) + 0.1y= 0.7
multiply 0.05 by all in parentheses
(0.05*10) + (0.05*-y) + 0.1y= 0.7
0.5 - 0.05y + 0.1y= 0.7
combine like terms
0.5 + 0.05y= 0.7
subtract 0.5 from both sides
0.05y= 0.2
divide both sides by 0.05
y= 4 # of nickels

CHECK:
If there were 10 coins and 4 are nickels, then 6 are dimes.

0.05x + 0.1y= 0.7
0.05(6) + 0.1(4)= 0.7
0.3 + 0.4= 0.7
0.7= 0.7

ANSWER: There are 4 nickels

Hope this helps! :)

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