,\left[x \right] = \left[ \frac{-2}{3}+\frac{\left( -4\right) \,y}{3}+\frac{z}{3}\right][x]=[3−2+3(−4)y+3z]
\left[X \right] = \left[ 5+6\,y - 2\,z\right][X]=[5+6y−2z]
\left[x \right] = \left[ 2+\frac{3\,y}{2}+\frac{ - z}{2}\right][x]=[2+23y+2−z]
system by elimination
You can solve this by convert mixed number(s) into improper fraction(s) 2. change both fractions to the equivalent fractions with the same denominator 3. omit denominators and write numerators as a ratio 4. simplify the ratio by dividing both numbers by the highest common factor.
I don’t see a diagram ? Just numbers...
(2x-3y)^5
(2x-3y)(2x-3y)(2x-3y)(2x-3y)(2x-3y)
1st and 2nd power :
(2x-3y)(2x-3y) = 2x(2x-3y)-3y(2x-3y) = 4x² - 6xy - 6xy + 9y²
= 4x² - 12xy + 9y²
3rd power:
(2x-3y)(4x² - 12xy + 9y²) = 2x(4x² - 12xy + 9y²) - 3y(4x² - 12xy + 9y²)
8x³ - 24x²y + 18xy² - 12x²y +36xy² - 27y³
8x³ - 24x²y - 12x²y + 18xy² + 36xy² - 27y³
8x³ - 36x²y + 54xy² - 27y³
4th power
(2x-3y)(8x³ - 36x²y + 54xy² - 27y³) = 2x(8x³ - 36x²y + 54xy² - 27y³) -3y(8x³ - 36x²y + 54xy² - 27y³) = 16x^4 - 72x³y + 108x²y² - 54xy³ - 24x³y + 108x²y² - 162xy³ + 81y^4
16x^4 - 72x³y - 24x³y + 108x²y² + 108x²y² - 54xy³ - 162xy³ + 81y^4
16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4
5th power
(2x-3y)(<span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
2x(</span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4) - 3y(<span>16x^4 - 96x³y + 216x²y² - 216xy³ + 81y^4)
= 32x^5 - 192x^4y + 432x</span>³y² - 432x²y³ + 162xy^4 - 48x^4y + 288x³y² - 648x²y³ + 648xy^4 - 243y^5
32x^5 - 192x^4y -48x^4y + 432x³y² + 288x³y² - 432x²y³ - 648x²y³ + 162xy^4 + 648xy^4 - 243y^5
32x^5 - 240x^4y + 720x³y² - 1,080x²y³ + 810xy^4 - 243y^5
Answer:
y=20,x=9
When doing problems like this it is important to always note: whatever you do to one side of the = sign you have to do to the other side.
Step-by-step explanation:
For this problem it helps that they already give you what y equals to so you can plug y in the top equation to figure out what x is. See attachment for step by step process