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2 years ago

Which ordered pair below is a solution to the following system of equations?

Mathematics

1 answer:

KatRina [158]2 years ago

3 0

The solution of the equation is given by (-2,-1), This is represented by option C.

<h3>What is a System of Equations?</h3>

A system of equations is a set of equation that have a common solution.

The solution of the equations can be determined by using the Elimination and Substitution method

3x-5y = -1

2x-y = -3

-7x = 14

x = -2

Substituting this value in the equation

3 * (-2) -5y = -1

-6 -5y = -1

-5y = 5

y = -1

Therefore, the solution of the equation is given by (-2,-1), This is represented by option C.

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Use cramers Rule to solve the following system:

Jet001 [13]

Answer:

The solution to the system is $x=1$ , $y=-2$ and $z=-5$

Step-by-step explanation:

Cramer's rule defines the solution of a system of equations in the following way:

$x= \frac{D_x}{D}$ , $y= \frac{D_y}{D}$ and $z= \frac{D_z}{D}$ where $D_x$ , $D_y$ and $D_z$ are the determinants formed by replacing the x,y and z-column values with the answer-column values respectively. $D$ is the determinant of the system. Let's see how this rule applies to this system.

The system can be written in matrix form like:

$\left[\begin{array}{ccc}5&-3&1\\0&2&-3\\7&10&0\end{array}\right]\times \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}6&11&-13\end{array}\right]$

Then each of the previous determinants are given by:

$D_x = \left|\begin{array}{ccc}6&-3&1\\11&2&-3\\-13&10&0\end{array}\right|=199$ Notice how the x-column has been substituted with the answer-column one.

$D_y = \left|\begin{array}{ccc}5&6&1\\0&11&-3\\7&-13&0\end{array}\right|=-398$ Notice how the y-column has been substituted with the answer-column one.

$D_z = \left|\begin{array}{ccc}5&-3&6\\0&2&11\\7&10&-13\end{array}\right|=-995$

Then, substituting the values:

$x= \frac{D_x}{D}=\frac{199}{199}\\ x=1$

$x= \frac{D_y}{D}=\frac{-398}{199}\\ y=-2$

$x= \frac{D_z}{D}=\frac{-995}{199}\\ x=-5$

3 0

3 years ago

HELP PLZ 5x + -9 + 3x - 20 =

Rama09 [41]

Add like terms. "Like terms" are those with the same constellation of variables.
.. terms with variable x: 5x +3x = (5 +3)x = 8x
.. terms with no variable: -9 -20 = -29

The simplified form is 8x -29.

6 0

3 years ago

Marvin used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer an

Llana [10]

For Marvin used the Quantitative Reasoning Process to build a budget while he is going to college. He worked hard over the summer and saved $2,595.9 to live on during the next two semesters of school. Marvin will receive a scholarship each semester for $958.35 money can Marvin spend each month, on average, for things like groceries, entertainment, and miscellaneous items is mathematically given as

$4512.6

<h3>How much money can Marvin spend each month, on average, for things like groceries, entertainment, and miscellaneous items?</h3>

Savings with Marvin = $2,595.9

Scholarship amount = $958.35

Total Scholarship amount received in 2 semesters = $958.35 X 2 = $ 1916.7

Now total money that Paolo have = (Savings with Marvin) + (Total Scholarship amount received in both semesters) = $2,595.9 + $1916.7 = $ 4512.6

Tuition & books cost = $2000

Tuition & books cost for 2 semesters = $2000 X 2 = $4000

Housing cost for 2 semester contract =$1,000

Total expenses in books and housing = $4000+ $1000 = $5000

Money left with Marvin after Total expenses in books and housing = $ 4512.6 - $5000 = −487.4

This means he has overspent.

as no. of months in 2 semesters = 8

Amount that Marvin would be in debt each month = −487.4/8 = −$60.925