Question

Solve the system using the elimination/addition method: 3x - 5y = 4 x - 4y = -1 The solution is (type in the x-coordinate first, then the y-coordinate): ) D Question 2 Determine if (-6, 9) is a solution of the system, 6x + y = -27 5x - y = -38 O No Yes Question 3 Determine if (2, 6) is a solution of the system, 0.6666666666666666 -0.26 O No o Yes Question 4 In this module, what way(s) was/were taught to solve systems of equations? Check all that apply- None of these Substitution Elimination Graphing Question 5 Solve the system of equations by substitution and write your answer as an ordered pair. 4x - 17y = -28 -2x + y = 14 The solution is (type in the x-coordinate first, then the y-coordinate): Question 6 1 pt Solve the system of equations by elimination and write your answer as an ordered pair. -3x – 2y = -15 - 4x + 2y = 36 The solution is (type in the x-coordinate first, then the y-coordinate): Question 7 1 pts At a store, five pairs of jeans and two shirts costs $213, while three pairs of jeans and four shirts costs $195. Find the cost of one shirt. $24 $35 O $21 $33 Question 10 Determine if (7,4) is a solution of the system, 3 -8 3 Yes O No

Answer 1

Question 1: The solution to the system using the elimination method is (3, 2).

Question 2: No, (-6, 9) is not a solution to the system.

Question 3: No, (2, 6) is not a solution to the system.

Question 4: The ways taught to solve systems of equations are Substitution, Elimination, and Graphing.

Question 5: The solution to the system by substitution is (5, 2).

Question 6: The solution to the system by elimination is (-3, 1).

Question 7: The cost of one shirt is $33.

Question 10: Yes, (7, 4) is a solution to the system.

Question 1: To solve the system using the elimination method, you can multiply the second equation by 5 to make the coefficients of \(y\) in both equations the same. The system becomes:


`\[\begin{align*}3x - 5y &= 4 \\5x - 20y &= -5\end{align*}\]\\`\[
\begin{align*}
3x - 5y &= 4 \\
5x - 20y &= -5
\end{align*}
\]

Now, add the two equations to eliminate \(y\). This results in \(8x = -1\), and solving for \(x\), you get \(x = -\frac{1}{8}\). Substitute this value back into either of the original equations, and you find \(y = \frac{17}{8}\). Therefore, the solution is \((-1/8, 17/8)\).

Question 2: To check if \((-6, 9)\) is a solution, substitute these values into both equations:

\[\begin{align*}6x + y &= -27 \\5x - y &= -38\end{align*}\]

After substitution, you'll see that both equations are satisfied, so the answer is "Yes."

Question 3: Substitute \(x = 2\) and \(y = 6\) into the given system:

\[
\begin{align*}
0.6666666666666666x - 0.26y &= 0 \\
\end{align*}
\]

The left side does not equal zero, so \((2, 6)\) is not a solution. The answer is "No."

Question 4: The ways taught to solve systems of equations are Substitution, Elimination, and Graphing.

Question 5: To solve the system by substitution, express \(y\) from the second equation and substitute it into the first equation. The solution is \(x = 5\) and \(y = 2\), so the answer is \((5, 2)\).

Question 6: To solve the system by elimination, add the two equations to eliminate \(y\). This results in \(x = -3\), and substituting this back, you get \(y = 1\). Therefore, the solution is \((-3, 1)\).

Question 7: Set up a system of equations based on the given information and solve for the cost of one shirt. The cost of one shirt is $33.

Question 10: Substitute \(x = 7\) and \(y = 4\) into the given system. The equations are satisfied, so the answer is "Yes."