Lance lived in portugal and brazil for a total of 14 months to learn portuguese. he learned an average of 130 new words per month when he lived in portugal, and an average of 150 new words per month when he lived in brazil. in total, he learned 1920 new words. write a system of equations to represent this situation. use x to represent portugal and y to represent brazil

He lived in Portugal 9 months and Brazil 5 months.

x = months in Portugal
y = months in Brazil

x + y = 14
130x + 150y = 1920

In the first equation, we will isolate x by subtracting y from both sides:
x + y - y = 14 - y
x = 14 - y

Now we will substitute this into the second equation:
130(14 - y) + 150y = 1920

Using the distributive property, 
130*14 - 130*y + 150y = 1920
1820 - 130y + 150y = 1920

Combining like terms,
1820 + 20y = 1920

Subtract 1820 from both sides:
1820 + 20y - 1820 = 1920 = 1820
20y = 100

Divide both sides by 20:
20y/20 = 100/20
y = 5

Now substitute this back into the first equation:
x + 5 = 14
x + 5 - 5 = 14 - 5
x = 9

He lived in Portugal 9 months and Brazil 5 months.

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