3 (x - 5) = 6solve for x
2 answers:
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Answer: y - 1 = –(x –7)
or y –5 = –1(x –3)
The attachment shows the graph of these equations (identical)
Step-by-step explanation:
The basic form for a point-slope equation is
y - b = m(x - a)
a is the x-value from the given coordinate, b is the y-value form the given coordinate, m is the slope. x and y are the variables in the function.
To find the slope, m, use the given coordinates. Get the difference in the y-values and divide by the difference in the x-values. This is "rise over run."
Subtract the first coordinate from the second coordinate.
Given coordinate points: (3,5) and (7,1) substitute values:
m= 1 –5 / 7 –3 becomes m= –4/4 so the slope, m = –4/4
That is –1 The "1" is "understood," so only the negative sign represents the slope in the equation
To write the equation: Take the basic form, substitute b and a values from either given coordinate. And use the value of m we just calculated.
y - b = m(x - a) Using the second coordinate: (7,1)
y - 1 = –(x –7)
or using the first coordinate:
y –5 = –(x –3)
Answer:
The system has infinitely many solutions.
Step-by-step explanation:
To find the solution for this system of linear equations you must:
Step 1: Transform the augmented matrix to the reduced row echelon form.
A matrix is a rectangular arrangement of numbers into rows and columns.
A system of equations can be represented by an augmented matrix.
In an augmented matrix, each row represents one equation in the system and each column represents a variable or the constant terms.
This is matrix that represents the system
The augmented matrix can be transformed by a sequence of elementary row operations to the matrix.
There are three kinds of elementary matrix operations.
- Interchange two rows (or columns).
- Multiply each element in a row (or column) by a non-zero number.
- Multiply a row (or column) by a non-zero number and add the result to another row (or column).
Using elementary matrix operations, we get that
Row Operation 1: Multiply the 1st row by -1/3
Row Operation 2: Multiply the 2nd row by -1/3
Row Operation 3: Add 4/3 times the 2nd row to the 1st row
Step 2: Interpret the reduced row echelon form
The reduced row echelon form of the augmented matrix is
which corresponds to the system
We see that the variables can take arbitrary numbers; they are called free variables. Let
,
. All solutions of the system are given by
The system has infinitely many solutions.