Question 1070318
{{{system(3x+5y=1+z,4x+7y=2-z)}}}


Make z as some constant:  k=z.


{{{system(3x+5y=1+k,4x+7y=2-k)}}}


Prepare to use Elimination.
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{{{system(12x+60y=12+12k,12x+21y=6-6k)}}}

Subtract second from first.

{{{39y=6+18k}}}

{{{13y=2+6k}}}

{{{highlight(y=(2+6k)/13)}}}
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{{{system(21x+35y=7+7k,20x+35y=10-5k)}}}
subtract second from first.
{{{highlight(x=-3+12k)}}}


k and z were made the same, so you can pick any real value for k (or z) and find the corresponding x and y values.  Infinitely many solutions to the three-variable, two-equation system.