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]);
This approach also allows you to construct something more interesting than a flat list, should that be desirable.