I was hoping that the named-capture variables would collect all of your matches, but they also only keep the last one, so as an alternative, I can only suggest embedded code (the (?:...)++ ensures no backtracking over your push @lhs code):

#!/usr/bin/perl
use 5.010;
use Data::Dumper;

my $equation = '979x + 87y - 8723z = 274320';
my @lhs;
die "match failed" unless $equation =~ /
    ^
    (?:
        (?<coeff>.*?) (?<var>[xyz])
            (?{ push @lhs, $+{coeff}, $+{var} })
    )++
    \s* = \s*
    (?<rhs>.*)
    $
    /ix;

my $rhs = $+{rhs};

say Dumper([\@lhs, $rhs]);
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This approach also allows you to construct something more interesting than a flat list, should that be desirable.