A system of equation is a collection of equations
The system of equation is: [tex]\mathbf{6x -y = 8}[/tex] and [tex]\mathbf{3x + 2y = 3 }[/tex]
The points are given as:
[tex]\mathbf{Line\ m = (0,-8)(1,-2)}[/tex]
[tex]\mathbf{Line\ n = (1,3)(3,0)}[/tex]
For line m
Calculate the slope
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{-2 + 8}{1 - 0}}[/tex]
[tex]\mathbf{m = \frac{6}{1}}[/tex]
[tex]\mathbf{m = 6}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y = 6(x - 0) -8}[/tex]
[tex]\mathbf{y = 6x -8}[/tex]
Rewrite as:
[tex]\mathbf{6x -y = 8}[/tex]
For line n
Calculate the slope
[tex]\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}[/tex]
So, we have:
[tex]\mathbf{m = \frac{0 - 3}{3 - 1}}[/tex]
[tex]\mathbf{m =- \frac{3}{2}}[/tex]
The equation is then calculated as:
[tex]\mathbf{y = m(x - x_1) + y_1}[/tex]
This gives
[tex]\mathbf{y =- \frac{3}{2}(x -0) + 3 }[/tex]
[tex]\mathbf{y =- \frac{3}{2}x + 3 }[/tex]
Multiply through by 2
[tex]\mathbf{2y =- 3x + 3 }[/tex]
Rewrite as:
[tex]\mathbf{3x + 2y = 3 }[/tex]
Hence, the system of equation is:
[tex]\mathbf{6x -y = 8}[/tex] and [tex]\mathbf{3x + 2y = 3 }[/tex]
Read more about system of equations at:
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