An equivalent fraction for 7 or 8 is 21 over 24
Answer:
x=4, y=1
Step-by-step explanation:
3.6x + 1.6y = 16
1.2x+3.2y = 8
Multiply the first equation by -2
-2(3.6x + 1.6y) = 16*-2
-7.2x -3.2y = -32
Add this to the second equation to eliminate y
-7.2x -3.2y = -32
1.2x+3.2y = 8
--------------------------
-6x = --24
Divide each side by -6
-6x/-6 = -24/-6
x=4
Now to find y
Multiply thesecond equation by -3
-3(1.2x+3.2y) = 8*-3
-3.6x -9.6y = -24
Add this to the first equation
-3.6x -9.6y = -24
3.6x + 1.6y = 16
---------------------------
-8y = -8
Divide each side by -8
y = 1
Step-by-step explanation:
To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Answer:
15. x = 4
16. a = 19
Step-by-step explanation:
"Cross multiply" essentially means "multiply both sides of the equation by the product of the denominators."
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<h3>15.</h3>
![\dfrac{x}{6}=\dfrac{2}{3}\\\\3(x)=6(2)\qquad\text{"cross multiply"}\\\\\boxed{x=4}\qquad\text{divide by 3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B6%7D%3D%5Cdfrac%7B2%7D%7B3%7D%5C%5C%5C%5C3%28x%29%3D6%282%29%5Cqquad%5Ctext%7B%22cross%20multiply%22%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D4%7D%5Cqquad%5Ctext%7Bdivide%20by%203%7D)
This is an example of a problem in which cross-multiplying introduces the need for an extra step: divide by 3. Had we simply multiplied by the denominator of the x-term, we would have been finished in one step:
x = 6(2/3) = 4
That is, rather than multiplying by the <em>product of the denominators</em>, sometimes the problem can be solved more easily if you multiply by their <em>least common multiple</em>.
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<h3>16.</h3>
![\dfrac{a+1}{a+5}=\dfrac{a-4}{a-1}\\\\(a-1)(a+1)=(a+5)(a-4)\qquad\text{"cross multiply"}\\\\a^2-1=a^2+a-20\qquad\text{simplify}\\\\\boxed{19=a}\qquad\text{add $20-a^2$}](https://tex.z-dn.net/?f=%5Cdfrac%7Ba%2B1%7D%7Ba%2B5%7D%3D%5Cdfrac%7Ba-4%7D%7Ba-1%7D%5C%5C%5C%5C%28a-1%29%28a%2B1%29%3D%28a%2B5%29%28a-4%29%5Cqquad%5Ctext%7B%22cross%20multiply%22%7D%5C%5C%5C%5Ca%5E2-1%3Da%5E2%2Ba-20%5Cqquad%5Ctext%7Bsimplify%7D%5C%5C%5C%5C%5Cboxed%7B19%3Da%7D%5Cqquad%5Ctext%7Badd%20%2420-a%5E2%24%7D)