Explanation
- Given the system of equations.
[tex] \begin{cases} y = - 4x \\ 23 - 5y = 44 \end{cases}[/tex]
- Substitute y = -4x in the second equation.
[tex]23 - 5( - 4x) = 44 \\ 23 + 20x = 44 \\ 20x = 44 - 23 \\ 20x = 21 \\ x = \frac{21}{20} [/tex]
- Substitute the value of x in any given equations. I will substitute the value of x in the first equation.
[tex]y = - 4x \Longrightarrow y = - 4( \frac{21}{20} ) \\ y = \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \Longrightarrow y = - \frac{21}{5} \\ y = - \frac{21}{5} [/tex]
- Answer Check by substituting both values in two equations.
First Equation
[tex]y = - 4x \Longrightarrow - \frac{21}{5} = - 4( \frac{21}{20} ) \\ - \frac{21}{5} = \cancel{ - 4}( \frac{21}{ \cancel{20}} ) \\ - \frac{21}{5} = - \frac{21}{5} \: \: \: \checkmark[/tex]
Second Equation
[tex]23 - 5y = 44 \\ 23 - 5( - \frac{21}{5} ) = 44 \\23 - \cancel{5}( - \frac{21}{ \cancel{5}} ) = 44 \\ 23 + 21 = 44 \\ 44 = 44 \: \: \: \: \checkmark[/tex]
Both equations are true for the value of x and value of y.
Answer
[tex] \begin{cases} x = \frac{21}{20} \\ y = - \frac{21}{5} \end{cases}[/tex]
Coordinate Point form
[tex]( \frac{21}{20} , - \frac{21}{5} )[/tex]
