Question

solve the system by graphing, substitution, or addition. enter your solution as an ordered pair (x,y) or select no solution or infinite number of solutions.\
\

$$\begin{cases}6x - 5y = 6\\\\x = 4y + 20\\end{cases}$$

\
\bigcirc\\ one or more solutions: \square\
\bigcirc\\ no solution\
\bigcirc\\ infinite number of solutions\
question help: \includegraphicsheight=1em{mailto.png} message instructor\
\boldsymbol{>} next question

Explanation:

Step1: Substitute \( x = 4y + 20 \) into \( 6x - 5y = 6 \)

Substitute \( x \) in the first equation: \( 6(4y + 20) - 5y = 6 \)

Step2: Expand and simplify the equation

Expand: \( 24y + 120 - 5y = 6 \)
Combine like terms: \( 19y + 120 = 6 \)
Subtract 120 from both sides: \( 19y = 6 - 120 = -114 \)

Step3: Solve for \( y \)

Divide both sides by 19: \( y = \frac{-114}{19} = -6 \)

Step4: Solve for \( x \) using \( x = 4y + 20 \)

Substitute \( y = -6 \): \( x = 4(-6) + 20 = -24 + 20 = -4 \)

Answer:

\((-4, -6)\)