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You drive $600$ miles in $2$ days. You drive $120$ miles less than you did on day one than on day $2$. How many miles did you drive both days separately? Solve algebraically.

$$d_1+d_2=600$$
$$d_2=d_1-120$$
Where do I go from here?

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    Try replacing your second equation for d2 into the first one...2011-04-17
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    Okay, so d1+d1-120=600?2011-04-17
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    So then, d1+d1=480. d1=240. But 240-120= 120, and 120+240 is not equal to 600.2011-04-17
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    $d_1 + d_1 - 120 = 600$ is correct, but you must *add* $120$ to each side, giving you $d_1 + d_1 = 720$, which should give you the right answer.2011-04-17
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    Neal, the problem is that you made a mistake, you should get $720$ instead of $480$ because you're adding $600 + 120$ not subtracting.2011-04-17

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In these types of situations, you want to write one variable explicitly in terms of the other plus any other constants sticking around.

In this case you have :
equation 1 $$d_1+d_2=600$$ and equation 2
$$d_2=d_1-120$$ So you can replace $d_2$ in equation 1 by $d_1-120$, giving you:
$$d_1+(d_1-120)=600$$
$$2d_1 = 720$$
$$d_1 = 360$$

Then plug in $360$ into the second equation to solve for $d_2$, namely:
$$d_2 = 360 - 120 = 240$$

Edit: It seems you understand how it works well. You just made an algebraic mistake. The hard part is usually coming up with the equation, which you don't seem to have any trouble with! :) Edit2: As stated in the comments, the algebraic mistake is that you are subtracting from both sides $120$ rather than adding $120$.