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saveliy_v [14]
3 years ago
15

Given the system of equations: 2x – y = –2 x = 14 + 2y What is the value of the system determinant? What is the value of the y−d

eterminant? What is the value of the x−determinant? What is the solution to the system of equations?
Mathematics
2 answers:
lbvjy [14]3 years ago
8 0

<u>ANSWER 1</u>

The given system  of equations is:

2x-y=-2

x=14+2y

Let us rewrite the second system to obtain,

2x-y=-2

x-2y=14

We need to apply the Cramer's rule. So we write out the coefficient matrices to obtain:

\left[\begin{array}{cc}2&-1\\1&-2\end{array}\right]


The answer column is;

\left[\begin{array}{c}-2&14\end{array}\right]


The value of the y-determinant is denoted by D_y. To find this we replace the coefficient determinant with answer-column values in y-column to get,

D_y=\left|\begin{array}{cc}2&-2\\1&14\end{array}\right|

Recall that,

If A=\left[\begin{array}{cc}a&b\\c&d\end{array}\right]

then, det_{A}=\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc

This implies that,

D_y=2\times14-1\times(-2)

D_y=28+2

D_y=30


<u>ANSWER 2</u>

The value of the x-determinant is denoted by D_x. To find this we replace the coefficient determinant with answer-column values in x-column to get,

D_x=\left|\begin{array}{cc}-2&-1\\14&-2\end{array}\right|


This implies that,

D_x=-2\times-2-14\times-1

D_x=4+14

D_x=18


<u>ANSWER 3</u>

To find the solution to the system of equations.


We need to find the determinant of the coefficient matrix.

D=\left|\begin{array}{cc}2&-1\\1&-2\end{array}\right|


This implies that,

D=2\times(-2)-1\times-1


D=-4+1


D=-3


Cramer's rule says that,

x=\frac{D_x}{D}


\Rightarrow x=\frac{18}{-3}


\Rightarrow x=-6


and


y=\frac{D_y}{D}


\Rightarrow y=\frac{30}{-3}


\Rightarrow y=-10


Therefore the solution is x=-6 and  y=-10.

sineoko [7]3 years ago
4 0
2x - y = -2

x = 14 + 2y

Plug in the x equation

2(14+2y) - y = -2

Distribute

28 + 4y - y = -2

Combine variables

28 + 3y = -2

Subtract 28 on both sides

3y = -30

Divide the y

y = -10

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