Answer Key 5.4
- a
a−b+2c=2+a+b+c=32a+3c=5a−b+2c=2+2a+b−c=2(3a+c=4)(−3)−9a−3c=−12−9a−3c=−12+2a+3c=5−7a−7=−7−7a=13a+c=43(1)+c=43+c=4−3−3c=1a+b+c=3(1)+b+(1)=3b+2=3−2−2b=1 - a
2a+3b−c=12+3a+4b+c=195a+7b=312a+3b−c=12+a−2b+c=−3(3a+b=9)(−7)−21a−7b=−635a+7b=31+−21a−7b=−63−16a−16=−32−16a=23a+b=93(2)+b=96+b=9−6−6b=3a−2b+c=−3(2)−2(3)+c=−32−6+c=−3−4+c=−3+4+4c=1 - a
(3x+y−z=7)(−1)−3x−y+z=−7+x+3y−z=5(−2x+2y=−2)(÷2)(−x+y=−1)(7)−7x+7y=−7(3x+y−z=7)(2)6x+2y−2z=14+x+y+2z=37x+3y=17+−7x+7y=−710y10=1010y=1−x+y=−1−x+(1)=−1−x+1=−1−1−1−x=−2x=2x+y+2z=3(2)+(1)+2z=32z+3=3−3−32z=0z=0 - a
x+y+z=4(−1)−x−y−z=−4−x−y−z=−4+x+2y+3z=10(y+2z=6)(2)2y+4z=12−x−y−z=−4+x−y+4z=20−2y+3z=16+2y+4z=127z7=287z=4y+2z=6y+2(4)=6y+8=6−8−8y=−2x+y+z=4x+(−2)+(4)=4x+2=4−2−2x=2 - a
x+2y−z=0+3x−2y−4z=−54x−5z=−5(2x−y+z=15)(2)4x−2y+2z=30+x+2y−z=0(5x+z=30)(5)25x+5z=1504x−5z=−5+25x+5z=15029x29=14529x=55x+z=305(5)+z=3025+z=30−25−25z=5x+2y−z=0(5)+2y−(5)=05+2y−5=02y=0y=0 - a
(x−y+2z=−3)(2)2x−2y+4z=−6+x+2y+3z=4(3x+7z=−2)(−1)−3x−7z=22x+y+z=−3+x−y+2z=−33x+3z=−6+−3x−7z=2−4z−4=−4−4z=13x+3z=−63x+3(1)=−63x+3=−6−3−33x3=−93x=−3x−y+2z=−3(−3)−y+2(1)=−3−3−y+2=−3−y−1=−3+1+1−y=−2y=2 - a
x+y+z=6+2x−y−z=−33x3=33x=1x−2y+3z=6(1)−2y+3z=61−2y+3z=6−1−1−2y+3z=5x+y+z=6(1)+y+z=61+y+z=6−1−1(y+z=5)(2)2y+2z=10−2y+3z=5+2y+2z=105z5=155z=3x+y+z=6(1)+y+(3)=61+y+3=6y+4=6−4−4y=2 - a
x+y−z=0+2x+y+z=03x+2y=0(x+y−z=0)(−4)−4x−4y+4z=0+x+2y−4z=0−3x−2y=0−3x−2y=0+3x+2y=00=0∴x=0y=0z=0 - a
x+y+z=2+2x−y+3z=93x+4z=112x−y+3z=9+y−z=−3(2x+2z=6)(−2)−4x−4z=−123x+4z=11+−4x−4z=−12−x=−1x=12x+2z=62(1)+2z=62+2z=6−2−22z2=42z=2x+y+z=2(1)+y+(2)=2y+3=2−3−3y=−1 - a
(4x+z=3)(2)8x+2z=6+6x−y−2z=−1(14x−y=5)(3)42x−3y=15+−2x+3y=540x40=2040x=12−2x+3y=5−2(12)+3y=5−1+3y=5+1+13y3=63y=24x+z=34(12)+z=32+z=3−2−2z=1 - a
x−z=−2+y+z=5x+y=32x−3y+z=−1+x−z=−2(3x−3y=−3)(÷3)x−y=−1+x+y=32x2=22x=1x−z=−2(1)−z=−21−z=−2−1−1−z=−3z=3y+z=5y+(3)=5y+3=5−3−3y=2 - a
(3x+4y−z=11)(2)6x+8y−2z=22+y+2z=−4(6x+9y=18)(÷3)2x+3y=6+−2x+y=−64y=0y=0−2x+y=−6−2x+0=−6−2x−2=−6−2x=3y+2z=−40+2z=−42z2=−42z=−2 - a
(−2y+z=−6)(3)−6y+3z=−18+x+6y+3z=30(x+6z=12)(−2)−2x−12z=−24+2x+2z=4−10z−10=−20−10z=22x+2z=42x+2(2)=42x+4=4−4−42x=0x=0−2y+z=−6−2y+2=−6−2−2−2y−2=−8−2y=4 - a
(x−y+2z=0)(2)2x−2y+4z=0+x+2y=13x+4z=1(2x+z=4)(−4)−8x−4z=−16+3x+4z=1−5x−5=−15−5x=3x+2y=13+2y=1−3−32y2=−22y=−12x+z=42(3)+z=46+z=4−6−6z=−2 - a
x+y+z=4+−y−z=−4x=0x−2y=00−2y=0−2y=0y=0−y−z=−40−z=−4−z=−4z=4 - a
(x+y−z=2)(−2)−2x−2y+2z=−4+2x+z=6−2y+3z=2+2y−4z=−4−z=−2z=22x+z=62x+2=6−2−22x2=42x=22y−4z=−42y−4(2)=−42y−8=−4+8+82y2=42y=2
