Solve the system of equations by substitution:

1. \( 7x - 2 = 2y \)
2. \( 3x = 2y - 1 \)

Possible solutions:
A. \((\frac{3}{4}, \frac{13}{8})\)
B. \((\frac{1}{4}, -\frac{1}{8})\)
C. No solution
D. Coincident

\left\{\begin{array}{ccc}7x-2=2y\\3x=2y-1\end{array}\right\\\\substitution:\\\\3x=7x-2-1\\3x-7x=-3\\-4x=-3\ \ \ /:(-4)\\x=\frac{3}{4}\\\\2y=7\cdot\frac{3}{4}-2=\frac{21}{4}-2=\frac{21}{4}-\frac{8}{4}=\frac{13}{4}\\2y=\frac{13}{4}\ \ \ \ /:2\\y=\frac{13}{8}\\\\Answer:x=\frac{3}{4};\ y=\frac{13}{8}.

Answered by Anonymous | 2024-06-10

To solve the given equations by substitution, we rearranged the first equation to express y in terms of x , substituted it into the second equation, solved for x and then substituted back to find y . The solution is ( 4 3 ​ , 8 13 ​ ) . Therefore, the correct option is A.
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Answered by Anonymous | 2024-12-23