{% set sectorSlug = craft.request.getSegment(2) %}
{% set socialServiceCategory = craft.categories.group('socialServices').slug(sectorSlug).first() %}
{% set socialServiceCategoryId = socialServiceCategory.id %}

{% set technologyCategoryIds = [] %}
{% if craft.request.getParam('type') %}
    {% set technologyCategoryIds = technologyCategoryIds|merge(craft.request.getParam('type')) %}
{% endif %}

{% set categoryIds = [socialServiceCategoryId]|merge(technologyCategoryIds) %}

{% set entries = craft.entries({
    section: 'solutions',
    relatedTo: {
        targetElement: ['and']|merge(categoryIds)
    }
}).order('listingType desc', 'title asc') %}

{# the above does *not* limit entries to socialServiceCategoryId #}