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Most Helpful Community Reply
If 5x = y +7, is (x – y) > 0?
1) xy = 6
2) x and y are consecutive integers with the same sign
Because the given statement xy = 6, and 5x = y + 7; we know that there will be 2 answer since xy = 6 is non-linear.
Therefore, statement 1 is not sufficient.
Since x and y are consecutive integers of the same sign, we can assign them x = x, y = x+1.
Therefore by plugging into the equation: we get -1<0, which means that (x-y) NOT > 0.
Thus, statement 2 is sufficient.
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Solve each of the
We can rewrite the equations as:
5x – y = 7
& x – y = - 1
For equation, 5x – y = 7
First, take x = 0 and find the value of y.
Then, take y = 0 and find the value of x.
Now similarly solve for equation, x – y = - 1
Plot the values in a graph and find the intersecting point for the solution.
Hence, the solution so obtained from the graph is (2,3), which is the intersecting point of the two lines.
The vertices of the formed triangle by these lines and the y - axis in the graph are A(2,3), B(0,1) and C(0, - 7).
Clearly, from the graph we can identify base and height of the triangle.
Now, we know
Area of Triangle =1/2 × base × height
Thus, Area(∆ABC) = 1/2 × 8 × 2
[∵Base = OB + OC = 1 + 7 = 8 units & height = 2 units from the y - axis to the point A]
Area(∆ABC) = 8 sq. units
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Solve Graphically the System of Equations 5x - Y = 7 X - Y + 1 = 0. Find the Coordinates of the Vertices of the Triangle Formed by These Two Lines and the Y-axis. - Mathematics
On a graph paper, draw a horizontal line X'OX and a vertical line YOY' as the x-axis and y-axis, respectively.
Graph of 5x - y = 7
5x - y = 7
⇒y = (5x – 7) …(i)
Putting x = 0, we get y = -7.
Putting x = 1, we get y = -2.
Putting x = 2, we get y = 3.
Thus, we have the following table for the equation 5x - y = 7.
Now, plot the points A(0, -7), B(1, -2) and C(2, 3) on the graph paper.
Join AB and BC to get the graph line AC. Extend it on both ways.
Thus, AC is the graph of 5x - y = 7.
Graph of x - y + 1 = 0
x - y + 1 = 0
⇒ y = x + 1 ……..(ii)
Putting x = 0, we get y = 1.
Putting x = 1, we get y = 2.
Putting x = 2, we get y = 3.
Thus, we have the following table for the equation x - y + 1 = 0.
Now, plot the points P(0, 1) and Q(1, 2). The point C(2, 3) has already been plotted. Join PQ and QC to get the graph line PC. Extend it on both ways.
Then, PC is the graph of the equation x - y + 1 = 0.
The two graph lines intersect at C(2, 3).
∴ The solution of the given system of equations is x = 2 and y = 3.
Clearly, the vertices of ΔAPC formed by these two lines and the y-axis are P(0, 1), C(2, 3) and A(0, -7).
Now, consider ΔAPC.
Here, height = 2 units and base (AP) = 8 units
∴ Area ΔAPC =` 1/2` × base × height sq. units
= `1/2` × 8 × 2
= 8 sq. units.
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7 y 2 5x
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