Question

bonus (2 points): notes are not allowed for the bonus. you can use desmos and a calculator only for the bonus. the solution of the following system is (6,2). find c and d. show your entire thought process and steps in working through this problem. 2x - dy = 6 cx + 4y = 14

Explanation:

Step1: Substitute x and y values into first - equation

Substitute \(x = 6\) and \(y = 2\) into \(2x−Dy = 6\).
\[2\times6−D\times2=6\]
\[12 - 2D=6\]

Step2: Solve for D

Subtract 12 from both sides:
\[- 2D=6 - 12\]
\[-2D=-6\]
Divide both sides by - 2:
\[D = 3\]

Step3: Substitute x and y values into second - equation

Substitute \(x = 6\) and \(y = 2\) into \(Cx + 4y=14\).
\[C\times6+4\times2=14\]
\[6C + 8=14\]

Step4: Solve for C

Subtract 8 from both sides:
\[6C=14 - 8\]
\[6C = 6\]
Divide both sides by 6:
\[C = 1\]

Answer:

\(C = 1\), \(D = 3\)