This study involves the investigation of silicon-carbon systems using ab initio techniques. It was motivated by the search for off-50:50 alloys and a way to quantify the strengths of 2D silicon-carbon materials. The study also predicts some under-reported properties for three previously proposed hypothetical allotropes of carbon. Preferably stable off-50:50 structures are identified from a set of trial structures for silicon-rich and carbon-rich candidates and their conditions of stability and physical properties are identified. A two-dimensional equation of state is introduced and applied to analyze the relative strengths of various 2D silicon-carbon materials. Of the possible off-50:50 alloy combinations and candidate structures considered, only the pyrite-FeS2, glitter-SiC2 and t-BC2 structures for SiC2 are elastically and dynamically stable. Analysis of the instability of Si2C reveals that it seems likely that carbon rich alloys are more favorable to their silicon-rich counterparts due to the smaller size of the carbon atoms and the more compact carbon-carbon bonds which result in less distorted bonding that is less metallic. The stiffness of the silicon dicarbide structures rank, in increasing order with 3C-SiC included for comparison, as glitter --> pyrite --> 3C-SiC --> t-SiC2. The moduli values for t-SiC2 are very comparable to 3C-SiC since for both materials, all atoms are four-fold coordinated with t-SiC2 having similar but slightly distorted, strong covalent tetrahedral bonding. The pyrite and glitter structures exhibit metallic character whereas t-SiC2 is a semi-conductor. Not only has this work demonstrated that, in principle, off-50:50 alloys of carbon and silicon are plausible, it has also provided information on how the strength and elastic properties of these materials are effected by increased silicon content. This has filled in a significant lack of knowledge about these bulk systems. For 2D systems, an equation of state is proposed that equates in-plane pressure with a change in surface area. It extracts the layer modulus as one of its fit parameters, which measures a material's resilience to hydrostatic stretching and predicts the material's intrinsic strength. Graphene is the most resilient to stretching with the highest intrinsic strength of all structures considered followed by SiC. Buckled Si is the least resilient with the lowest strength. An off-50:50 planar alloy, called silagraphene, differs elastically from SiC but has a comparable strength due to the similarity of their layer modulus. The novel 2D equation of state presented here opens up new ways to study and compare the strength properties of mono or multi-layered 2D materials, especially how their resilience to isotropic stretching responds to in-plane pressure.