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Lesson: Challenging Problem Solving - 08t03

Advanced Algebra: Example 3

[Page 8 of 37]
Review the following question and then proceed to the task below.

 

If 2x + 3y = 26 and 7x – 5y = 60, then x + y =

–12
–8
8
10
12
Which of the following Problem Solving approaches can be used to solve the question above? Select Yes or No and then click Continue.
  YES NO
Backsolving:
Picking Numbers:
Algebra:
Use your algebraic knowledge to solve the equation system below. Click Continue to confirm your answer.

2x + 3y = 26

7x – 5y = 60

In order to force a variable to cancel out, we must make one set of coefficients match—either both x terms or both y terms. We can do this by multiplying each equation by an appropriate number:

Now that our y terms have the same coefficient, we can add our equations. Note that we are adding in this case because our y coefficients, although equal in value, have opposite signs—one is positive and one is negative:

Since we know x, we can plug this value into our first equation to find y:

Since x + y = 10 + 2 = 12, Choice (E) is correct.

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