Mathematics: 6. Solve using any method. x+6y=7 5x + 8y = 13

The answer would be -3 13/81 (simplified)...

6. Solve using any method. x+6y=7 5x + 8y = 13

Ответ:

xojade

23.01.2022

Mathematics

x = 1, y = 1 → (1, 1)

Step-by-step explanation:

$\bold{ELIMINATION\ METHOD}\\\\\left\{\begin{array}{ccc}x+6y=7&\text{Multiply both sides by (-5)}\\5x+8y=13\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-5x-30y=-35\\5x+8y=13\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-22y=-22\qquad\text{divide both sides by (-22)}\\.\qquad\boxed{y=1}\\\\\text{Put it to the first equation}\\\\x+6(1)=7\\x+6=7\qquad\text{subtract 6 from both sides}\\\boxed{x=1}$

$\bold{SUBSTITUTION\ METHOD}\\\\\left\{\begin{array}{ccc}x+6y=7&\text{subtract}\ 6y\ \text{from both sides}\\5x+8y=13\end{array}\right\\\\\left\{\begin{array}{ccc}x=7-6y&(1)\\5x+8y=13&(2)\end{array}\right\\\\\text{Substitute (1) to (2):}\\\\5(7-6y)+8y=13\qquad\text{use the distributive property}\\(5)(7)+(5)(-6y)+8y=13\\35-30y+8y=13\qquad\text{subtract 35 from both sides}\\-30y+8y=13-35\qquad\text{combine like terms}\\-22y=-22\qquad\text{divide both sides by (-22)}\\\boxed{y=1}$

$\text{Put it to (1):}\\\\x=7-6(1)\\x=7-6\\\boxed{x=1}$

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6. Solve using any method.
x+6y=7
5x + 8y = 13

Ответ:

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