1.
The first equation of a linear system is \(2x+3y=52\). Choose a second equation to form a linear system with infinite solutions.
Solution: Infinite solutions require the same line. Multiply \(2x+3y=52\) by -5 to get \(-10x-15y=-260\).
2.
The first equation of a linear system is \(-6x+12y=-42\). Choose a second equation to form a linear system with no solution.
Solution: No solution means parallel lines. Original line: \(y=\frac12x-\frac72\). Choice D gives \(y=\frac12x+\frac{21}{2}\). Same slope, different intercept.
3.
Use the graph to approximate the solution of this linear system:
Solution: The intersection point of the two lines on the graph is approximately (-2.1, -1.2).
4.
Determine the number of solutions for the linear system that models this problem: Two people are playing a game. The difference in their points is 83. When the number of points each player has is doubled, the difference is 166.
Solution: Let scores be p and q. \(p=q+83\) and \(2p=2q+166\). The second equation simplifies to the first, so there are infinite solutions.
5.
Which linear system is represented by this graph?
Solution: One line has equation \(y=x-5\), which is \(x-y=5\). The other has intercept 3 and slope \(-5/6\), giving \(5x+6y=18\).
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