Let's solve the system of linear equations using the Cramer's rule.
Δ=∣∣132−32−56−52∣∣==1⋅2⋅2+(−3)⋅(−5)⋅2+6⋅3⋅(−5)−−6⋅2⋅2−1⋅(−5)⋅(−5)−(−3)⋅3⋅2==4+30−90−24−25+18=−87;
Δ1=∣∣21−30−6−32−56−52∣∣==21⋅2⋅2+(−3)⋅(−5)⋅(−6)+6⋅(−30)⋅(−5)−−6⋅2⋅(−6)−21⋅(−5)⋅(−5)−(−3)⋅(−30)⋅2==84−90+900+72−525−180=261;
Δ2=∣∣13221−30−66−52∣∣==1⋅(−30)⋅2+21⋅(−5)⋅2+6⋅3⋅(−6)−−6⋅(−30)⋅2−1⋅(−5)⋅(−6)−21⋅3⋅2==−60−210−108+360−30−126=−174;
Δ3=∣∣132−32−521−30−6∣∣==1⋅2⋅(−6)+(−3)⋅(−30)⋅2+21⋅3⋅(−5)−−21⋅2⋅2−1⋅(−30)⋅(−5)−(−3)⋅3⋅(−6)==−12+180−315−84−150−54=−435;
x=ΔΔ1=−87261−3;y=ΔΔ2=−87−174=2;z=ΔΔ3=−87−435=5;x+y+z=−3+2+5=4.
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