Strengthen Your Systems of Equations Skills

The reduced row echelon form of a system of linear equations is given. Write the system of equations corresponding to the given matrix. Use x,y.x,y. or x,y,z.x,y,z. or $x_1,x_2,x_3,x_4$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $\left[\begin{array}{cccc}1& 0& 2& -1\\ 0& 1& -4& -2\\ 0& 0& 0& 0\end{array}\right]$

Consider the system of equations described by
$\{\begin{array}{l}{x}_1=2x_1-3x_2\\ x_2=4x_1-5x_2\end{array}$
1. Write down the system of equations in matrix form.
2. Find the eigenvalues of the system of equations.
3. Find the associated eigenvectors.

Solve the system of equations by hand.

$\{\begin{array}{l}-3x+y=2\\ 9x-3y=-6\end{array}$

Solve the system of equations by hand.
$\{\begin{array}{l}5x-4y=-5\\ 3x+y=14\end{array}$

Solve the system of equations by hand.
$\{\begin{array}{l}x+4y=-2\\ -2x+12y=9\end{array}$

Solve the system of equations
$\{\begin{array}{l}-7x+6y=20\\ 2x-3y=2\end{array}$

Two lines , P and Q , are graphed:

x+y=2x+2y=11
3x+3y=62x+4y=22
x+y=2x+2y=11
3x+3y=62x+4y=22
Two systems of equations are shown. Which TWO of the following statements each provide sufficient reasoning to show that the systems have the same solution?
The two equations in the second system are multiples of the two equations in the first system. A)
The two constant terms in the second system are multiples of the two equations in the first system. B)
The graphs of the equations in the first system coincide with the graphs of the equations in the second system. C)
The slopes of the graphs of the equations in the first system are equivalent to the slopes of the graphs of the equations in the second system. D)
The x -intercepts of the graphs of the equations in the first system coincide with the x -intercepts of the graphs of the equations in the second system. E)

Write $y=13x+7$ in standard form using integers.

a. $-2x+3y=21$

b. $3x-2y=21$

c. $-2x-3y=21$

Solve the system of equations $2x+3y=5$
$5x-4y=2$

Solve the system by clennaton $2x-y=0$
$3x-2y=-3$
The solution is ( . )

Which system of equations is not a linear system?
a) $2x+y=11$
$x=13+y$
b) $2x=11-y$
$4x-y=13$
c) ${\displaystyle -\frac{1}{2}x-y=\frac{3}{4}}$
${\displaystyle \frac{3}{2}x+2=-\frac{7}{8}}$
d) ${\displaystyle -x²+y=10}$
$x+y=5$

Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems below. include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.
${\displaystyle y=x^2+6x+9}$
$x+y=3$

Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems below. include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable.
$x-3y=7$
$-3x+4y=-1$

Solve $\{\begin{array}{l}(x-3{)}^2+(y+1{)}^2=5\\ x-3y=7\end{array}$

Write and solve a system of equations for each situation. Check your answers
A shop has one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.50. If you buy 5 bags and spend $17, how many of each size bag did you buy?

To find the equation:

$-2y+y=6$
$4x-2y=5$

What is the solution of the system of equations?
$y=2x-3$
$5x+y=11$
$A(2,1)$
$B(1,2)$
$C(3,-4)$
$D(1,-1)$

Manuel has $54 to buy CDs and books. Each CD costs $9, and each book costs $6. He wants to buy exactly 7 items to spend all of his money. Write a system of equations that could be solved to determine the number of CDs and the number of books Manuel buys.

$10-3=36$
$2+5=-4$
solve using substitution