1.
Which linear system has the solution \(x=-2\) and \(y=6\)?
Substitute \(x=-2\) and \(y=6\) into both equations of each system and check which system makes both equations true.
2.
Car A left Calgary at 8 A.M. to travel \(500\) mi. to Regina at an average speed of \(63\) mph. Car B left Regina at the same time to travel to Calgary at an average speed of \(37\) mph. A linear system that models this situation is \(d=500-63t\) and \(d=37t\). Which graph would you use to determine how far the cars are from Regina when they meet? What is this distance?
Set the two distance equations equal: \(500-63t=37t\). Then find \(t\) and substitute into \(d=37t\).
3.
Which graph represents the solution of the linear system: \(-3x-y=-5\) and \(4x-y=2\)?
Solve or check the intersection point. The correct graph should show the two lines intersecting at the solution of the system.
4.
Solve the linear equations by substitution: \(4(x+1)-2\left(y+\frac{1}{2}\right)=0\) and \(5(x+1)-2y=10\).
First simplify the first equation to isolate \(y\), then substitute the expression for \(y\) into the second equation.
5.
Use substitution to solve this problem: Wai Sen scored \(85\%\) on part A of a math test and \(95\%\) on part B of the math test. Her total mark for the test was \(70\). The total mark possible for the test was \(78\). How many marks is each part worth?
Let \(a\) be Part A and \(b\) be Part B. Use \(a+b=78\) and \(0.85a+0.95b=70\), then substitute.
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