Given the system of equations, what is the solution?5x - 4y = 7x = 5 - 3/2y

Mathematics

1 answer:

nignag [31]3 years ago

8 0

9514 1404 393

Answer:

(x, y) = (61/23, 36/23)

Step-by-step explanation:

We assume you intend the equations to be ...

5x -4y = 7
x = 5 -3/2y

Then in general form, they are ...

5x -4y -7 = 0

2x +3y -10 = 0

The solution using the "cross multiplication method" is ...

1/(15 +8) = x/(40+21) = y/(-14 +50)

(x, y) = (61/23, 36/23)

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Comment on "cross multiplication method"

When the coefficients from the general form equations are written as a 2×4 array with the first and last columns the same ...

$\left\{\begin{array}{cccc}5&-4&-7&5\\2&3&-10&2\end{array}\right\}$

the solution is 1/d1 = x/d2 = y/d3, where d1, d2, d3 are the determinants of successive pairs of columns.

d1 = (5)(3) -(2)(-4)
d2 = (-4)(-10) -(3)(-7)
d3 = (-7)(2) -(-10)(5)

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laila [671]

Answer:

See attached

Step-by-step explanation:

When there is a lot of repetitive calculation to do, I like to let a spreadsheet or graphing calculator do it. The attached shows a spreadsheet that computes all the values you're asked to find.

For a linear equation in standard form, ax +by = c

the x-intercept is: c/a
the y-intercept is: c/b
the slope is: m = -a/b

Of course, the slope-intercept form of the equation is ...

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and the values of the various points on the graph can be computed from that equation.

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You will note that the last two equations describe the same line.

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Note on spreadsheet formulas

When you put the formulas into the spreadsheet, make sure to fix the column number or row number of the values you're computing, as appropriate. For example, the y-values in the different columns always use the slope from the slope column (fixed), the y-intercept from that column (fixed), and the x-value from the top row (fixed). If you make the cell references relative instead of fixed, you will get wrong answers.