2100020404
Level:
A
The system of two linear equations can be represented graphically by two lines. Decide which of the pictures corresponds the following system.
\[\begin{aligned}
-x+3y&=3.5\\
1.4x+y&=2.9\\
\end{aligned}
\]
Systems of linear equations and inequalities
2100020405
Level:
A
Provided that the missing parts of lines were completed, which of the pictures would depict solution of the system if solved graphically?
\[\begin{aligned}
x-7y&=-9\\
3x-2y&=11\\
\end{aligned}\]
9000007206
Level:
A
Consider the linear system:
\[
\begin{aligned}2x - 3y - 12& = 0,&
\\\text{???}\quad & = 0.
\\ \end{aligned}
\]
In the following list, identify the missing second equation if you know that the system
does not have a solution.
\(- 6x + 9y - 9 = 0\)
\(2x + 3y - 6 = 0\)
\(- 4x + 6y + 24 = 0\)
\(x + 2y - 12 = 0\)
9000023901
Level:
A
Solve the following system and write the solution as the ordered pair
\([x,y]\).
\[\begin{aligned}
x + y & = -1 & &
\\x - y & = 5 & &
\end{aligned}\]
\([2;-3]\)
\([-2;1]\)
\([3;-2]\)
\([-3;2]\)
9000023902
Level:
A
Solve the following system and write the solution as the ordered pair
\([x,y]\).
\[\begin{aligned}
2x + y & = 2 & &
\\x + 2y & = 7 & &
\end{aligned}\]
\([-1;4]\)
\([2;-2]\)
\([1;3]\)
\([3;-4]\)
9000023903
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = -2, & &
\\3x - 2y & = 10. & &
\end{aligned}\]
Find \(5x + y\).
\(8\)
\(- 12\)
\(- 8\)
\(12\)
9000023904
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
4x - 3y & = -3, & &
\\x + 2y & = 13. & &
\end{aligned}\]
Find \(2x - 7y\).
\(- 29\)
\(- 41\)
\(- 11\)
\(31\)
9000023905
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 5y & = 7, & &
\\ - 4x - 3y & = 7. & &
\end{aligned}\]
In the following list identify a true statement.
\(x^{2} + y^{2} = 25\)
\(x^{2} + y^{2} = 7\)
\(x^{2} - y^{2} = -7\)
\(y^{2} - x^{2} = 7\)
9000023906
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
2x + 3y & = 4, & &
\\4x + 6y & = 9. & &
\end{aligned}\]
In the following list identify a true statement.
The system does not have any solution.
\(x < y\)
\(x > y\)
\(x = y\)
9000023907
Level:
A
Let \([x;y]\)
be the solution of the system
\[\begin{aligned}
- x + 2y & = 6, & &
\\2x + 3y & = 2. & &
\end{aligned}\]
In the following list identify a true statement.
\(|x| = |y|\)
\(|x| < |y|\)
\(|x| > |y|\)
The system does not have any solution.