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- Let the unknown be a variable.
- Translate the statement into an equation.
- Solve and verify in options.
Correct Answer: A
Correct Answer: A
Method / Topic: Algebra
The answer satisfies the equation formed from the question.
Short Explanation
Detailed Explanation
Correct Answer: A
Method / Topic: Algebra
<table cellspacing="0" style="border-collapse:collapse; height:20px; width:85px">
<tbody>
<tr>
<td style="background-color:#c0e6f5; border-bottom:1px solid #44b3e1; border-left:none; border-right:none; border-top:1px solid #44b3e1; height:20px; vertical-align:top; white-space:normal; width:85px"><span style="color:#000000">From x−y=1, y=x−1. Substitute into 3x+2y=18: 3x+2(x−1)=18, so 5x−2=18, 5x=20, and x=4. Then y=3, which satisfies both equations. The calculation is checked against the conditions in the
. A useful final check is to substitute the
s involving signs, denominators, amount versus interest, and distance versus speed.</span></td>
</tr>
</tbody>
</table>
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Learn + Solve: Shortcut, Trap & Fast Route Click to view shortcut, steps, and common mistake
Shortcut used, common trap, and the fastest solving route
- Let the unknown be a variable.
- Translate the statement into an equation.
- Solve and verify in options.
If 3x+2y=18 and x−y=1, find x.
Explanation
Correct Answer: A
Method / Topic: Algebra
The answer satisfies the equation formed from the question.
Short Explanation
Detailed Explanation
Correct Answer: A
Method / Topic: Algebra
<table cellspacing="0" style="border-collapse:collapse; height:20px; width:85px">
<tbody>
<tr>
<td style="background-color:#c0e6f5; border-bottom:1px solid #44b3e1; border-left:none; border-right:none; border-top:1px solid #44b3e1; height:20px; vertical-align:top; white-space:normal; width:85px"><span style="color:#000000">From x−y=1, y=x−1. Substitute into 3x+2y=18: 3x+2(x−1)=18, so 5x−2=18, 5x=20, and x=4. Then y=3, which satisfies both equations. The calculation is checked against the conditions in the
. A useful final check is to substitute the
s involving signs, denominators, amount versus interest, and distance versus speed.</span></td>
</tr>
</tbody>
</table>
See full explanation + shortcut trick
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