Problem

E. x0
Question 7
The solution of the two simultaneous equations 2ax+2by=3 and 3ax2by=7 for x and y is:
A. x=2a,y=34a22b
B. x=2,y=34a2b
C. x=0,y=0
D. x=3a,y=7b
E. x=2a,y=12b
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Answer

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Answer

The solution is x=3+b22a,y=12b

Steps

Step 1 :Multiply the first equation by 3 and the second equation by 2 to make the coefficients of y equal:

Step 2 :6ax + 6by = 9,

Step 3 :6ax - 4by = 14.

Step 4 :Subtract the second equation from the first equation:

Step 5 :10by = -5 \Rightarrow y = -\frac{1}{2}b.

Step 6 :Substitute y back into the first equation:

Step 7 :2ax + 2b\left(-\frac{1}{2}b\right) = 3 \Rightarrow 2ax - b^2 = 3.

Step 8 :Divide both sides by 2a:

Step 9 :x = \frac{3 + b^2}{2a}.

Step 10 :The solution is x=3+b22a,y=12b

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