Respuesta :
Answer:
(a) The system of the equations [tex]\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.[/tex] has no solution.
(b) The system of the equations [tex]\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.[/tex] has many solutions [tex]y=\frac{2x}{3}-\frac{5}{3}[/tex]
Step-by-step explanation:
(a) To find the solutions of the following system of equations [tex]\left \{ {2x-3y\:=3} \atop {4x-6y\:=3}} \right.[/tex] you must:
Multiply [tex]2x-3y=3[/tex] by 2:
[tex]\begin{bmatrix}4x-6y=6\\ 4x-6y=3\end{bmatrix}[/tex]
Subtract the equations
[tex]4x-6y=3\\-\\4x-6y=6\\------\\0=-3[/tex]
0 = -3 is false, therefore the system of the equations has no solution.
(b) To find the solutions of the system [tex]\left \{ {4x-6y\:=10} \atop {16x-24y\:=40}} \right.[/tex] you must:
Isolate x for [tex]4x-6y=10[/tex]
[tex]x=\frac{5+3y}{2}[/tex]
Substitute [tex]x=\frac{5+3y}{2}[/tex] into the second equation
[tex]16\cdot \frac{5+3y}{2}-24y=40\\8\left(3y+5\right)-24y=40\\24y+40-24y=40\\40=40[/tex]
The system has many solutions.
Isolate y for [tex]4x-6y=10[/tex]
[tex]y=\frac{2x}{3}-\frac{5}{3}[/tex]
