9514 1404 393
Answer:
Step-by-step explanation:
The general approach here is to choose a variable you want to eliminate, identify the coefficients of it, and use those to multiply the equations so adding the products will eliminate the variable.
Here, the coefficients of x are -1 and -3; the coefficients of y are 2 and 5. We often like to choose the set of coefficients that includes 1 or where the coefficients are related by an integer factor. These criteria suggest that we should use the coefficients -1 and -3. One of our multipliers must be the opposite of one of these coefficients. So, we choose for them to be -3 and +1.
That is, multiplying the first equation by -3 will make the x-coefficient be 3; multiplying the second equation by 1 will make the x-coefficient be -3. Adding these equations will then eliminate x terms.
(-3)(-x +2y = 12)
<u>+ </u><u>(1)</u><u>(-3x +5y =27)</u>
<u>gives</u> (3x -6y) +(-3x +5y) = -36 +27
which simplifies to the sum ...
0x -1y = -9
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Dividing by the coefficient of y, we find y = 9. Substituting into the first equation, we have ...
-x +2(9) = 12)
x = 18-12 = 6
The solution is (x, y) = (6, 9).
