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Solve the linear system
1).5x + 4y = 16 
y = -16 

2). 3x + 6y = 15 
-2x + 3y = -3 

3). 7y = -14x + 42 
7y = 14 x + 14 

Sagot :

deathstrike001
1.5x+4y=16
5x+4(-16)=16
5x-64=16
5x=80
x=16

2.3x+6y=15
-2x+3y=-3

Multiply the 2nd equation by 2

3x+6y=15
-4x+6y=-6
7x=9
x=9/7

3x+6y=15
3(9/7)+6y=15
27/7+6y=15
6y=78/7
y=78/42 or 39/21 or 13/7

3.7y = -14x + 42 
7y = 14 x + 14

-14x+42=14x+14
-28x=-28
x=1
Lilith
[tex]1)\\ \\\begin{cases} 5x + 4y = 16 \\ y=-16\end{cases} \\ \\ \begin{cases} 5x + 4*(-16) = 16 \\ y=-16\end{cases} \\ \\ \begin{cases} 5x -64 = 16 \\ y=-16\end{cases}[/tex]

[tex]\begin{cases} 5x = 16 +64\\ y=-16\end{cases} \\ \\ \begin{cases} 5x =80/:5 \ \\ y=-16\end{cases} \\ \\ \begin{cases} 5x = 16 +64\\ y=-16\end{cases} \\ \\ \begin{cases} x =16\\ y=-16\end{cases}[/tex]



[tex]2)\\ \\\begin{cases} 3x+6y=15 \\ -2x + 3y = -3 \end{cases} \\ \\\begin{cases} 3x = 15-6y \ /:3 \\ -2x + 3y = -3 \end{cases} \\ \\ \begin{cases} x = 5-2y \\ -2*(5-2y) + 3y = -3 \end{cases} \\ \\\begin{cases} x = 5-2y \\ -10+4y + 3y = -3 \end{cases} \\ \\[/tex]

[tex]\begin{cases} x = 5-2y \\ 7y = -3+10 \end{cases} \\ \\ \begin{cases} x = 5-2y \\ 7y = 7 \ /:7\end{cases} \\ \\ \begin{cases} x = 5-2 *1 \\ y =1 \end{cases} \\ \\ \begin{cases} x = 3 \\ y = 1 \end{cases} \\ \\[/tex]



[tex]3)\\ \\\begin{cases} 7y = -14x + 42 \\ 7y = 14 x + 14 /:7 \end{cases} \\ \\\begin{cases} 7*(2x+2) = -14x + 42 \\ y = 2 x + 2 \end{cases} \\ \\ \begin{cases} 14x+14 = -14x + 42 \\ y = 2 x + 2\end{cases} \\ \\ \begin{cases} 14x+ 14x = 42 -14 \\ y = 2 x + 2 \end{cases}[/tex]

[tex]\begin{cases} 28x = 28 \ /:28 \\ y = 2 x + 2 \end{cases}\\ \\\begin{cases} x = 1 \\ y = 2 *1+ 2\end{cases}\\ \\\begin{cases} x = 1 \\ y = 4 \end{cases}[/tex]


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