1)
\[
5x - 2y = 4
\]
2)
\[
3x - 5y = 13
\]
\[
x - 2y = 5
\]
\[
3x + y = 9
\]
Answer (2)
\left\{\begin{array}{ccc}5x-2y=4\\3x+y=9&/\cdot2\end{array}\right\\+\left\{\begin{array}{ccc}5x-2y=4\\6x+2y=18\end{array}\right\\----------\\.\ \ \ \ \ 11x=22\ \ \ \ /:11\\.\ \ \ \ \ \ \ x=2\\\\3\cdot2+y=9\\6+y=9\\y=9-6\\y=3\\\\Answer:x=2;\ y=3
\left\{\begin{array}{ccc}3x-5y=13\\x-2y=5\end{array}\right\\\left\{\begin{array}{ccc}3x-5y=13\\x=2y+5\end{array}\right\\\\substitute:\\\\3(2y+5)-5y=13\\6y+15-5y=13\\y=13-15\\y=-2\\\\x=2\cdot(-2)+5=-4+5=1\\\\Answer:x=1;\ y=-2.
The solutions to the pairs of equations given by the student can be found using either the substitution or elimination method. For the first pair, the solution is ( x , y ) = ( − 19 6 , − 19 53 ) . For the second pair, the solution is ( x , y ) = ( 7 23 , − 7 6 ) .
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