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# Algebra 1 Item No 59

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• 1. Algebra 1 Item No. 59
• Find the intersection of lines
• x – y = 1 and 2x – y = 5.
• A. (-1, -2)
• B. (0, -1)
• C. (0, 1)
• D. (4, 3)
www.upcatreview.com
• 2.
• The intersection of two lines is a point which is a solution to the two equations.
x + y = 3 2x – y = 3 (2, 1) www.upcatreview.com
• 3.
• The intersection of two lines is a point which is a solution to the two equations.
x + y = 3 2x – y = 3 (2, 1) That means that we can use the coordinates of the point of intersection as x and y values for both equations 2 + 1 = 3 3 = 3 2(2) – 1 = 3 3 = 3 www.upcatreview.com
• 4.
• To obtain the intersection of the two lines, we can use any of the following methods:
• Graphing
• Substitution
• Elimination
www.upcatreview.com
• 5.
• To obtain the intersection of the two lines, we can use any of the following methods:
• Graphing
• Substitution
• Elimination
The crudest of all the methods… thus it’s not advisable to use this one. The easiest to remember www.upcatreview.com
• 6.
• To obtain the intersection of the two lines, we can use any of the following methods:
• Graphing
• Substitution
• Elimination
The crudest of all the methods… thus it’s not advisable to use this one. The easiest to remember We’ll use this one to solve the problem www.upcatreview.com
• 7.
• In elimination, as the name implies, we eliminate one of the variables.
x – y = 1 2x – y = 5 We can try to eliminate y for this problem www.upcatreview.com
• 8.
• In elimination, as the name implies, we eliminate one of the variables.
x – y = 1 2x – y = 5 result: an equation with only one variable We can try to eliminate y for this problem Elimination is done by adding or subtracting the two equations www.upcatreview.com
• 9.
• To eliminate y and have only x in our final equation, let’s subtract the two equations
x – y = 1 2x – y = 5 – – x = – 4 x = 4 www.upcatreview.com
• 10.
• Now, we will use the value of x which we got from the previous solution…
x = 4 www.upcatreview.com
• 11.
• Now, we will use the value of x which we got from the previous solution…
• … and substitute it to any of the given equation and solve for the unknown.
x = 4 x – y = 1 We will use the first given equation because it’s a lot simpler www.upcatreview.com
• 12.
• Now, we will use the value of x which we got from the previous solution…
• … and substitute it to any of the given equation and solve for the unknown.
x = 4 x – y = 1 4 – y = 1 – y = 1 – 4 y = 3 We will use the first given equation because it’s a lot simpler www.upcatreview.com
• 13.
• The intersection of the two lines is the point with the following values:
• Thus, the coordinates of the point of intersection is (4, 3).
x = 4 y = 3 www.upcatreview.com
• 14.