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方程组与方程解的个数挑战

\( nx+3t=-3x+4n \) 
In the given equation, \( n \) and \( t \)are constants. The equation has no solution. What CANNOT be the value of \( n+t \)?
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2025年8月美国A卷 · 原库模块 1 · Q16作答 ↗
方程组与方程解的个数进阶

\( \frac{2}{5}x+\frac{7}{5}y=\frac{2}{7} \) 
\( gx+ky=\frac{5}{2} \) 
In the given system of equations, g and k are constants. The system has infinitely many solutions. What is the value of \( \frac{g}{k} \)?
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Bluebook试题7 · 原库模块 3 · Q14作答 ↗
方程组与方程解的个数基础

y = 6x + 18One of the equations in a system of two linear equations is given. The system has no solution. Which equation could be the second equation in the system?
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机考OG2 · 原库模块 2 · Q19作答 ↗
方程组与方程解的个数进阶

\( 30x=1,800y-2,700 \) 
One of the two equations in a system of linear equations is given. The system has no solution. Which equation could be the second equation in this system?
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2024年10月北美B卷 · 原库模块 2 · Q17作答 ↗
方程组与方程解的个数进阶

\( \frac{4}{5}x+\frac{6}{5}y=g \) 
\( \frac{8}{13}x+hy=k \) 
In the given system of equations, g, h, and k are constants. The system has infinitely many solutions. What is the value of \( \frac{g}{k} \)?
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2024年11月北美A卷 · 原库模块 2 · Q19作答 ↗
方程组与方程解的个数进阶

5x+3y=6
The given equation is one equation in a system of two linear equations. If the system of equations has at least one solution, which of the following equations could be the other equation in the system?
I.     7.5x+4.5y=9
II.    7.5x-4.5y=9

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2025年9月国际A卷 · 原库模块 2 · Q21作答 ↗
方程组与方程解的个数进阶

4x - 6y = 10y +2
ty= \(\frac{1}{2}\)+2x
In the given system of equations,t is a constant. If the system has no solution, what is the value of t?
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Bluebook试题1 · 原库模块 3 · Q17作答 ↗
方程组与方程解的个数进阶

\( \frac{12x+16}{4}-\frac{s}{13}=r\left(x-9\right) \) 
In the given equation, s and r are constants, and \( s>0. \) If the equation has infinitely many solutions, what is the value of s?
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2024年10月A卷 · 原库模块 2 · Q16作答 ↗
方程组与方程解的个数进阶

\( -\frac{3}{19}rx+\frac{s}{8}=10-\frac{5}{57}x \) 
In the given equation, r and s are constants. The equation has no solution. What is the value of r?
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25年10月国际C卷练习 · 原库模块 2 · Q9作答 ↗
方程组与方程解的个数进阶

3x+5y=89x+15y=24For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?
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2023年6月A卷 · 原库模块 2 · Q21作答 ↗
方程组与方程解的个数基础

\( -12x+14y=36 \) 
\( -6x+7y=-18 \) 
How many solutions does the given system of equations have?
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PSAT10 P2 · 原库模块 2 · Q22作答 ↗
方程组与方程解的个数进阶

\( 7x+6y=5 \) 
\( 28x+24y=20 \) 
For each real number r, which of the following points lies on the graph of each equation in the xy-plane for the given system?
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Bluebook试题7 · 原库模块 3 · Q20作答 ↗