8. Solving systems of linear equations[1]

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1、Solvingsystemsoflinearequations1.z+w−3=k6z−10w=8Considerthesystemofequationsabove,wherekisaconstant.Forwhichvalueofkarethereinfinitelymany(w,z)solutions?A.B.5C.8D.NoneoftheaboveCorrectanswer:DDifficultylevel:22.−5x−4y=2a4x−5y=2Whichofthefollowingchoicesofaw

2、illresultinasystemoflinearequationswithexactlyonesolution?A.acanbeanynumberB.acanbeanynumberexcept0.8C.acanbeanynumberexcept−0.8D.a=0.8Correctanswer:ADifficultylevel:23.Considerthesystemofequationsabove.Whichofthefollowingstatementsaboutthissystemistrue?A.T

3、hereisonlyone(x,y)solutionandx+yispositive.B.Thereisonlyone(x,y)solutionandx+yisnegative.C.Thereareinfinitelymany(x,y)solutions.D.Thereareno(x,y)solutions.Correctanswer:CDifficultylevel:24.Considerthesystemofequationsabove.Whichofthefollowingstatementsistru

4、e?A.Thereisonlyonesolution(x,y)andx+yispositive.B.Thereisonlyonesolution(x,y)andx+yisnegative.C.Thereareinfinitelymanysolutions.D.Therearenosolutions.Correctanswer:BDifficultylevel:25.1.70p−0.34q=00.17(q+1)−0.85(p−1)=0Considerthesystemofequationsabove.Howma

5、ny(p,q)solutionsdoesthissystemhave?A.0B.1C.InfinitelymanyD.NoneoftheaboveCorrectanswer:ADifficultylevel:26.3s+2t−3=c−7s−5t=4Considerthesystemofequationsabove,wherecisaconstant.Forwhichvalueofcisthereexactlyone(s,t)solutionwheres=−1?A.B.C.D.NoneoftheaboveCor

6、rectanswer:ADifficultylevel:27.0.7a−0.8b=−0.1a−1.4=−6(b−0.1)Considerthesystemofequationsabove.If(a,b)isthesolutiontothesystem,thenwhatisthevalueofthesumofaandb?A.B.C.D.Correctanswer:DDifficultylevel:28.6(1−a)=3(a−b)+14(b−2)=3aConsiderthesystemofequationsabo

7、ve.If(a,b)isthesolutiontothesystem,thenwhatisthevalueof?A.B.C.D.Correctanswer:DDifficultylevel:29.7p=9(p+q)+119q+3=−4(7q+p)Considerthesystemofequationsabove.If(p,q)isthesolutiontothesystem,thenwhatisthevalueofp+q?Correctanswer:-9Difficultylevel:210.−0.2x+by

8、=7.25.6x−0.8y=4Considerthesystemofequationsabove.Forwhatvalueofbwillthesystemhaveexactlyonesolution(x,y)withx=2?Roundtheanswertothenearesttenth.Correctanswer:0.8Difficultylevel:311.−4a−5b−4=−21−2b+5a−1