Respuesta :
Answer:
The solutions to the system of equations are [tex]y=4,\:x=5[/tex].
Step-by-step explanation:
To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]
First,
[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]
[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]
Subtract the first equation from the second equation
[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]
Solve [tex]-9y=-36[/tex] for y:
[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]
For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x
[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]
The solutions to the system of equations are:
[tex]y=4,\:x=5[/tex]
