x = -1
Step-by-step explanation:
![{4}^{5x} = {2}^{2(5x)} = {2}^{10x}](https://tex.z-dn.net/?f=%20%7B4%7D%5E%7B5x%7D%20%20%3D%20%20%7B2%7D%5E%7B2%285x%29%7D%20%20%3D%20%20%7B2%7D%5E%7B10x%7D%20)
![{( \frac{1}{32}) }^{(1 - x)} = {2}^{ - 5(1 - x)} = {2}^{(5x - 5)}](https://tex.z-dn.net/?f=%20%7B%28%20%5Cfrac%7B1%7D%7B32%7D%29%20%7D%5E%7B%281%20-%20x%29%7D%20%20%3D%20%20%7B2%7D%5E%7B%20-%205%281%20-%20x%29%7D%20%20%3D%20%20%7B2%7D%5E%7B%285x%20-%205%29%7D%20)
or
![{2}^{10x} = {2}^{(5x - 5)}](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7B10x%7D%20%20%3D%20%20%7B2%7D%5E%7B%285x%20-%205%29%7D%20)
Since both sides have the same base, we can write
10x = 5x - 5
or
5x = -5
x = -1
According to the system:
5 – 7x + 2y² = -10
1 – 5x – 2y = -22
______________
a) No ; (4, 6) is not a solution to the
system. This point does not touch either equation.
b) No ; (6, 4) is not a solution to the system. This point does not touch either equation.
Solutions:
![( \frac{122 - 3 \sqrt{101}}{25}, \frac{ - 7 +3 \sqrt{101}}{10}) ≈ (3.674, 2.315) \\ ( \frac{122 + 3 \sqrt{101}}{25}, \frac{ - 7 - 3 \sqrt{101}}{10}) ≈ (6.086, -3.715)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B122%20-%203%20%5Csqrt%7B101%7D%7D%7B25%7D%2C%20%5Cfrac%7B%20-%207%20%2B3%20%5Csqrt%7B101%7D%7D%7B10%7D%29%20%E2%89%88%20%283.674%2C%202.315%29%20%5C%5C%20%28%20%5Cfrac%7B122%20%20%2B%20%203%20%5Csqrt%7B101%7D%7D%7B25%7D%2C%20%5Cfrac%7B%20-%207%20%20-%203%20%5Csqrt%7B101%7D%7D%7B10%7D%29%20%E2%89%88%20%286.086%2C%20-3.715%29%20)
x = ( 122 ∓ 3√101 ) / 25 ≈ 3.674 or 6.086
y = ( -7 ± 3√101 ) / 10 ≈ 2.315 or -3.715
Answer:
Step-by-step explanation:
lets solve for x
flip the equation
add-4 to both sides
divide both sides by 3
x=1/3y+-4/3