Perform calculations related to a system of two linear equations.
Author: shiroeExecutions: 26
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Enter a, b, e, c, d, and f as fractions.
Enter a non-zero number in the denominator.
Enter a non-zero number in the numerator for a, b, c, and d.
Neither input nor output supports mixed fractions.
Format for the system of equations to be entered:
ax + by = e
cx + dy = f
Enter a non-zero number in the denominator.
Enter a non-zero number in the numerator for a, b, c, and d.
Neither input nor output supports mixed fractions.
Format for the system of equations to be entered:
ax + by = e
cx + dy = f
| The value of a | (Decimal Format) |
| The value of b | (Decimal Format) |
| Value of e | (Decimal Format) |
| Value of c | (Decimal Format) |
| Value of d | (Decimal Format) |
| Value of f | (Decimal Format) |
| m1 | (The coefficient of x in "y = ~") (decimal format) |
| n1 | (Constant term (y-intercept) in "y = ~") (decimal format) |
| m2 | (The coefficient of x in "y = ~") (decimal format) |
| n2 | (Constant term (y-intercept) in "y = ~") (decimal format) |
| Are the two lines parallel? | (yes=1, no=0) |
| Are the two lines the same (do they overlap)? | (yes=1, no=0) |
| x-numerator | |
| x denominator | |
| y-molecule | |
| y denominator | |
| Value of x | Numerator/Denominator (decimal format) |
| Value of y | Numerator/Denominator (decimal format) |
R6 (2024). April 14 (Sun)_“Systems of Two Linear Equations” Ver. 001
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The equations are in the form:
ax + by = e
cx + dy = f
We will transform both equations into the form “y = ~” and, when visualizing them as graphs in the xy-plane,
examine whether the two lines are parallel or whether they are the same line and overlap.
The equations take the form:
y = m1x + n1
y = m2x + n2
where n1 and n2 are the y-intercepts.
m1 and m2 are the slopes of the lines. If the slopes are equal, the lines are parallel.
Furthermore, if the y-intercepts are equal, the two lines are identical and coincide.
Here, we do not use inverse matrices, nor do we use the sweep method with the scale factor matrix.
First, we eliminate y, solve for x, and then substitute it into y = m1x + n1.
If the lines are not parallel, the solution (x, y) is output.
We do not handle cases where there is no solution, an indeterminate solution, or an arbitrary constant.
We do not handle complex numbers (non-real numbers with a non-zero imaginary part).