Question 235375
The Setup
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Equation 1: {{{40*X + 58*Y = 646}}}
Equation 2: {{{X + Y = 13}}}

Solution:
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Solve equation 2 for one of the variables.  I picked X.
{{{X + Y = 13}}} Rewrite
{{{X = 13 - Y}}}
Now plug (13 - Y) in for X in equation 1
{{{40*X + 58*Y = 646}}}
{{{40*(13 - Y) + 58*Y = 646}}} Multiply the 40 by (13 - Y) and rewrite
{{{520 - 40Y + 58Y = 646}}} Combine like terms
{{{520 + 18Y = 646}}} Subtract 520 from both sides
{{{18Y = 126}}} Divide both sides by 18
{{{Y = 7}}}
Now we know the the truck driver went 58mph for 7 hours.

Check Answer:
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Plug 7 into equation 2 for Y
{{{X + Y = 13}}}
{{{X + 7 = 13}}} Subtract 7 from both sides
{{{X = 6}}}
Now go back to equation 1 and plug 7 in for Y, and use 6 for X.
{{{40*X + 58*Y = 646}}}
{{{40*6 + 58*7 = 646}}} Simplify
{{{240 + 406 = 646}}}
{{{646 = 646}}}