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歡迎您訪問數(shù)學(xué)考題練習(xí):已知方程組的解為且|k|<2,則a-b的取值范!

數(shù)學(xué)考題練習(xí):已知方程組的解為且|k|<2,則a-b的取值范

更新時(shí)間:2024-01-12 16:41:12作者:貝語網(wǎng)校

已知方程組的解為且|k|<2,則a-b的取值范圍是________.

試題答案

0<a-b<4

試題解析

把k看作常數(shù)利用加減消元法求出x、y,即a、b的值,然后用k表示出a-b,再根據(jù)|k|<2進(jìn)行計(jì)算即可得解.

解答:,

②×3得,9x-3y=3k+12③,

①+③得,14x=14,

解得x=1,

把x=1代入②得,3-y=k+4,

解得y=-k-1,

∵方程組的解是,

∴a=1,b=-k-1,

∴a-b=1-(-k-1)=1+k+1=k+2,

∵|k|<2,

∴-2<k<2,

∴0<k+2<4.

即0<a-b<4.

故答案為:0<a-b<4.

點(diǎn)評:本題考查了二元一次方程組的解,把k看作常數(shù)求出方程組的解是解題的關(guān)鍵,要學(xué)會并熟練進(jìn)行|k|<2的變形.

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