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A first number plus twice a second number is 8. Twice the first number plus the second totals 10. Find the numbers.

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[tex]\{ {{x+2y=8\ \ \ \ \ \ \ \ \ \ \ } \atop {2x+y=10\ [\times\ (-2)]}}\\\\ \{ { {\ \ x+2y=8\ \ } \atop {-4x-2y=-20}}\\\\ -3x=-12\\ x=\frac{-12}{-3}\\ \boxed{x=4}\\\\ 2(4)+y=10\\ 8+y=10\\ y=10-8\\ \boxed{y=2}\\\\ x+2y=8\\ 4+2(2)=8\\ 4+4=8\\ \boxed{8=8}\\\\ 2(4)+2=10\\ 8+2=10\\ \boxed{10=10}[/tex]
a + 2b = 8
2a + b = 10
b = 10 - 2a
a + 2(10 - 2a) = 8
a + 20 - 4a = 8
-3a = -12
a = 4
4 + 2b = 8
2b = 4
B = 2
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