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Answers
1)Therefore, the equation Ax + By + C = 0 represents a line with slope -A/B and y-intercept -C/B. This represents a line parallel to the Y axis (explained here). This represents a line parallel to the X axis (explained here).
2)Therefore, the equation Ax + By + C = 0 represents a line with slope -A/B and y-intercept -C/B. This represents a line parallel to the Y axis (explained here). This represents a line parallel to the X axis (explained here). In each case, the equation Ax + By + C = 0 represented a straight line.
3)What you have here are two equations:
x+y=5 [1]
x−y=10 [2]
To solve for x and y , you should rearrange one of the equations for one of the variables x or y . Choose equation [1] to rearrange for y , because it is easy to do so.
y=5−x [3]
Now, substitute this expression into equation [2]:
x(5−x)=6
Now use this equation to solve for x . Firstly expand the parentheses:
5x−x2=6
Rearrange the terms so that they are all on one side of the equation:
x2−5x+6=0
What you have here is a quadratic equation. There are many ways to solve a quadratic equation but I will choose the easiest method for this problem.
Factorise the quadratic expression on the left-hand side of the equation by using the product-sum method (or by decomposition):
(x−2)(x−3)=0
The null factor law gives x=2 or x=3 as the solution.
Now, substitute x=2 or x=3 into equation [3] to get the value of y:
when x=2 , then y=5−2=3
when x=3 , then y=5−3=2
Therefore, there are two solutions to these simultaneous equations, which are: (2,3) and (3,2) ■
1)Therefore, the equation Ax + By + C = 0 represents a line with slope -A/B and y-intercept -C/B. This represents a line parallel to the Y axis (explained here). This represents a line parallel to the X axis (explained here).
2)Therefore, the equation Ax + By + C = 0 represents a line with slope -A/B and y-intercept -C/B. This represents a line parallel to the Y axis (explained here). This represents a line parallel to the X axis (explained here). In each case, the equation Ax + By + C = 0 represented a straight line.
3)What you have here are two equations:
x+y=5 [1]
x−y=10 [2]
To solve for x and y , you should rearrange one of the equations for one of the variables x or y . Choose equation [1] to rearrange for y , because it is easy to do so.
y=5−x [3]
Now, substitute this expression into equation [2]:
x(5−x)=6
Now use this equation to solve for x . Firstly expand the parentheses:
5x−x2=6
Rearrange the terms so that they are all on one side of the equation:
x2−5x+6=0
What you have here is a quadratic equation. There are many ways to solve a quadratic equation but I will choose the easiest method for this problem.
Factorise the quadratic expression on the left-hand side of the equation by using the product-sum method (or by decomposition):
(x−2)(x−3)=0
The null factor law gives x=2 or x=3 as the solution.
Now, substitute x=2 or x=3 into equation [3] to get the value of y:
when x=2 , then y=5−2=3
when x=3 , then y=5−3=2
Therefore, there are two solutions to these simultaneous equations, which are: (2,3) and (3,2) ■