Question 1:
For this case we must solve the following system of equations by the method of elimination:
[tex]8x-6y=-20\\-16x+17y=30[/tex]
We multiply the first equation by 2:
[tex]16x-12y = -40[/tex]
We have the equivalent system:
[tex]16x-12y = -40\\-16x + 17y = 30[/tex]
We add the equations:
[tex]5y = -10[/tex]
We divide between 5 on both sides of the equation:
[tex]y = - \frac {10} {5}\\y = -2[/tex]
We find the value of the variable "x":
[tex]8x-6 (-2) = - 20\\8x + 12 = -20\\8x = -20-12\\8x = -32[/tex]
We divide by 8 on both sides of the equation:
[tex]x = - \frac {32} {8}\\x = -4[/tex]
Thus, the solution of the system is:
[tex](x, y): (- 4, -2)[/tex]
Answer:
[tex](x, y): (- 4, -2)[/tex]
Question 2:
For this case we must solve the following system of equations by the method of elimination:
[tex]-4y-11x = 36\\20 = -10x-10y[/tex]
We multiply the first equation by 10:
[tex]-40y-110x = 360[/tex]
We multiply the second equation by -4:
[tex]40y + 40x = -80[/tex]
We have the equivalent system:
[tex]-40y-110x = 360\\40y + 40x = -80[/tex]
We add the equations:[tex]-70x = 280[/tex]
We divide by -70 on both sides of the equation:
[tex]x = \frac {280} {- 70}\\x = -4[/tex]
We find the value of the variable "y":
[tex]-4y-11 (-4) = 36\\-4y + 44 = 36\\-4y = 36-44\\-4y = -8[/tex]
We divide between -4 on both sides of the equation:
[tex]y = - \frac {8} {- 4}\\y = 2[/tex]
Thus, the solution of the system is:
[tex](x, y): (- 4,2)[/tex]
Answer:
[tex](x, y): (- 4,2)[/tex]
