Answer:
The solution to the system of equations will be:
[tex]x=0,\:y=-\frac{11}{5}[/tex]
Step-by-step explanation:
Given the expression
[tex]x - 5y = 11[/tex]
[tex]3x - 5y = 11[/tex]
solving the expression
[tex]\begin{bmatrix}x-5y=11\\ 3x-5y=11\end{bmatrix}[/tex]
Multiplying x-5y = 11 by 3: 3x-15y=33
so
[tex]\begin{bmatrix}3x-15y=33\\ 3x-5y=11\end{bmatrix}[/tex]
and
[tex]3x-5y=11[/tex]
[tex]-[/tex]
[tex]\underline{3x-15y=33}[/tex]
[tex]10y=-22[/tex]
now solving 10y = -22 for y
[tex]10y=-22[/tex]
divide both sides by 10
[tex]\frac{10y}{10}=\frac{-22}{10}[/tex]
simplify
[tex]y=-\frac{11}{5}[/tex]
For 3x-5y=11 plug in y = -11/5
[tex]3x-15\left(-\frac{11}{5}\right)=33[/tex]
[tex]3x+15\cdot \frac{11}{5}=33[/tex]
[tex]3x+33=33[/tex]
Subtract 33 from both sides
[tex]3x+33-33=33-33[/tex]
Simplify
[tex]3x=0[/tex]
Divide both sides by 3
[tex]\frac{3x}{3}=\frac{0}{3}[/tex]
Simplify
[tex]x=0[/tex]
Thus, the solution to the system of equations will be:
[tex]x=0,\:y=-\frac{11}{5}[/tex]
