Explanation
- Given the system of equations.
[tex] \begin{cases} y = 4x - 9 \\ y = x - 3 \end{cases}[/tex]
We can combine both equations
[tex]4x - 9 = x - 3[/tex]
Solve the equation.
[tex]4x - x = 9 - 3 \\ 3x = 6 \\ x = \frac{6}{3} \longrightarrow \frac{2}{1} \\ x = 2[/tex]
Then we substitute the value of x in any given equations which I will be substituting in the second equation
[tex]y = x - 3 \\ y = 2 - 3 \\ y = - 1[/tex]
Therefore, from x = 2 and y = -1, the solution is (2,-1)
Answer Check
Substitute the value of x and y in both equations.
First Equatio
[tex]y = 4x - 9 \\ - 1 = 4(2) - 9 \\ - 1 = 8 - 9 \\ - 1 = - 1[/tex]
Second Equation
[tex]y = x - 3 \\ - 1 = 2 - 3 \\ - 1 = - 1[/tex]
Both equations are true for (2,-1).
Answer
[tex] \begin{cases} x = 2 \\ y = - 1 \end{cases} \\ \sf \underline{coordinate} \\ (2,-1)[/tex]
