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stiks02 [169]
3 years ago
9

What is the solution to the system of equations 2x+y=2 and y= -2x-2?

Mathematics
1 answer:
finlep [7]3 years ago
5 0

Answer:

NO SOLUTION

Step-by-step explanation:

Solve this system by substitution:

Replace y in the first equation with -2x - 2:

2x + (-2x - 2) = 2, or

2x - 2x - 2 = 2

0 = 4      This is not possible, so this system has NO SOLUTION.

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For the following linear system, put the augmented coefficient matrix into reduced row-echelon form.
Anni [7]

Answer:

The reduced row-echelon form of the linear system is \left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right]

Step-by-step explanation:

We will solve the original system of linear equations by performing a sequence of the following elementary row operations on the augmented matrix:

  1. Interchange two rows
  2. Multiply one row by a nonzero number
  3. Add a multiple of one row to a different row

To find the reduced row-echelon form of this augmented matrix

\left[\begin{array}{cccc}2&3&-1&14\\1&2&1&4\\5&9&2&7\end{array}\right]

You need to follow these steps:

  • Divide row 1 by 2 \left(R_1=\frac{R_1}{2}\right)

\left[\begin{array}{cccc}1&3/2&-1/2&7\\1&2&1&4\\5&9&2&7\end{array}\right]

  • Subtract row 1 from row 2 \left(R_2=R_2-R_1\right)

\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\5&9&2&7\end{array}\right]

  • Subtract row 1 multiplied by 5 from row 3 \left(R_3=R_3-\left(5\right)R_1\right)

\left[\begin{array}{cccc}1&3/2&-1/2&7\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right]

  • Subtract row 2 multiplied by 3 from row 1 \left(R_1=R_1-\left(3\right)R_2\right)

\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&3/9&9/2&-28\end{array}\right]

  • Subtract row 2 multiplied by 3 from row 3 \left(R_3=R_3-\left(3\right)R_2\right)

\left[\begin{array}{cccc}1&0&-5&16\\0&1/2&3/2&-3\\0&0&0&-19\end{array}\right]

  • Multiply row 2 by 2 \left(R_2=\left(2\right)R_2\right)

\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&-19\end{array}\right]

  • Divide row 3 by −19 \left(R_3=\frac{R_3}{-19}\right)

\left[\begin{array}{cccc}1&0&-5&16\\0&2&3&-6\\0&0&0&1\end{array}\right]

  • Subtract row 3 multiplied by 16 from row 1 \left(R_1=R_1-\left(16\right)R_3\right)

\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&-6\\0&0&0&1\end{array}\right]

  • Add row 3 multiplied by 6 to row 2 \left(R_2=R_2+\left(6\right)R_3\right)

\left[\begin{array}{cccc}1&0&-5&0\\0&1&3&0\\0&0&0&1\end{array}\right]

8 0
3 years ago
Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes o
Volgvan

Answer:

\frac{4}{15} \\

Step-by-step explanation:

number of the students like brussels sprouts but dislike lima beans = number of these students who dislike lima beans - number of students who dislike lima beans and also dislike brussels sprouts

\frac{2}{3}-\frac{3}{5}* \frac{2}{3} = \frac{2}{3}-\frac{6}{15}=\frac{10}{15}-\frac{6}{15}=\frac{4}{15}\\

8 0
3 years ago
Is 4y^2*3y^5=12y^10 true or false.
mixer [17]

Answer:False

Step-by-step explanation:#UwU God

5 0
3 years ago
What slope would make the lines<br> parallel?<br> y = -3x + 9<br> y = [?]x + 4
Vladimir79 [104]

Answer:

- 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 9 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus

y = - 3x + 4 ← is the equation of a parallel line

4 0
3 years ago
What are the steps to solving this problem K + 8\5 = 1k
DaniilM [7]

-- Subtract K from each side of the equation.

8/5 = 0

-- There is no value for K that can make this a true statement. So the original equation has no solution.

8 0
3 years ago
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