Answer:
Ax + Ay + 2A = 0 for any nonzero A, for example (A=1): x + y + 2 = 0
Step-by-step explanation:
The equation of a line is
Ax + By + C = 0
so we know that:
A*-3 + B*1 + C = 0
A*5 + B*-7 + C = 0
Let's subtract one from the other:
A*(-3 - 5) + B*(1 + -7) = 0
A*-8 + B*8 = 0
B*8 = A*8
B = A
Let's input B = A into the first two equations
A*-3 + A*1 + C = A*-2 + C = 0
A*5 + A*-7 + C = A*-2 + C = 0
checks out
C = 2A
So for any nonzero A the equation of
Ax + Ay + 2A = 0 produces a line passing between the points. Example would be
x + y + 2 = 0
Answer:
3/4
Step-by-step explanation:
I'm actually not sure about this, probably don't put this in so you don't get it wrong.
Answer:
The extraneous solution is 4.
Step-by-step explanation:
First, let us calculate the value of 'x' without squaring both side of the expression. This is illustrated below:
-5 = 3x - 7
Collect like terms
-5 + 7 = 3x
2 = 3x
Divide both side by 3
x = 2/3.
Now, let us calculate the value of 'x' by squaring both side of the expression. This is illustrated below:
(-5)^2 = (3x - 7)^2
25 = (3x - 7)(3x - 7)
25 = 9x^2 - 21x - 21x + 49
9x^2 - 42x + 49 - 25 = 0
9x^2 - 42x + 24 = 0
Solving by factorisation:
Multiply the first term i.e 9x^2 and 3rd term i.e 24 together. The result is 216x^2.
Next, we shall obtain two factors of 216x^2 such that when we add them together, it will give the 2nd term i.e -42x in the equation. These factors are: -6x and -36x
Now we can write the above equation as:
9x^2 - 42x + 24 = 0
9x^2 - 6x - 36x + 24 = 0
3x(3x - 2) - 12(3x - 2) = 0
(3x - 12)(3x - 2) = 0
3x - 12 = 0 or 3x - 2 = 0
3x = 12 or 3x = 2
x = 12/3 or x = 2/3
x = 4 or 2/3.
We can see that when we solve the question without squaring both side, the value of x is 2/3. But when we solve by squaring both side, the value of x are 4 and 2/3.
Therefore, the extraneous solution to the question is 4.
Without converting the equations to the same form, the property that must be different in the functions is the slope
<h3>How to determine the difference in the properties of the functions?</h3>
From the question, the equations are given as
y = x + 5
y + x = 5
From the question, we understand that:
The equations must not be converted to the same form before the question is solved
The equation of a linear function is represented as
y = mx + c
Where m represents the slope and c represents the y-intercept
When the equation y = mx + c is compared to y = x + 5, we have
Slope, m = 1
y-intercept, c = 5
The equation y = mx + c can be rewritten as
y - mx = c
When the equation y - mx = c is compared to y + x = 5, we have
Slope, m = -1
y-intercept, c = 5
By comparing the properties of the functions, we have
- The functions have the same y-intercept of 5
- The functions have the different slopes of 1 and -1
Hence, the different properties of the functions are their slopes
Read more about linear functions at
brainly.com/question/15602982
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