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3 years ago

2x+y=5 , 3x+2y=8 solve using cross multiplication

Mathematics

1 answer:

Xelga [282]3 years ago

5 0

Answer:

x=2

y=1

Step-by-step explanation:

2x+y=5

3x+2y= 8

<=> 6x+3y=15

6x+4y=16

<=> -y=-1

2x+y=5

<=> y=1

2x+1=5

<=> y=1

2x=4

<=> y=1

x=2

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Irina18 [472]

Step-by-step explanation:

Hey there!

By looking at the figure, the given "2x" and "6x + 28" are co-interior angle.

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3 years ago

Solve the following equations. log2(x^2 − 16) − log^2(x − 4) = 1

Alenkasestr [34]

Answer:

$x=\frac{4*(2+e)}{e-2}$

Step-by-step explanation:

Let's rewrite the left side keeping in mind the next propierties:

$log(\frac{1}{x} )=-log(x)$

$log(x*y)=log(x)+log(y)$

Therefore:

$log(2*(x^{2} -16))+log(\frac{1}{(x-4)^{2} })=1\\ log(\frac{2*(x^{2} -16)}{(x-4)^{2}})=1$

Now, cancel logarithms by taking exp of both sides:

$e^{log(\frac{2*(x^{2} -16)}{(x-4)^{2}})} =e^{1} \\\frac{2*(x^{2} -16)}{(x-4)^{2}}=e$

Multiply both sides by $(x-4)^{2}$ and using distributive propierty:

$2x^{2} -32=16e-8ex+ex^{2}$

Substract $16e-8ex+ex^{2}$ from both sides and factoring:

$-(x-4)*(-8-4e-2x+ex)=0$

Multiply both sides by -1:

$(x-4)*(-8-4e-2x+ex)=0$

Split into two equations:

$x-4=0\hspace{3}or\hspace{3}-8-4e-2x+ex=0$

Solving for $x-4=0$

Add 4 to both sides:

$x=4$

Solving for $-8-4e-2x+ex=0$

Collect in terms of x and add $4e+8$ to both sides:

$x(e-2)=4e+8$

Divide both sides by e-2:

$x=\frac{4*(2+e)}{e-2}$

The solutions are:

$x=4\hspace{3}or\hspace{3}x=\frac{4*(2+e)}{e-2}$

If we evaluate x=4 in the original equation:

$log(0)-log(0)=1$

This is an absurd because log (x) is undefined for $x\leq 0$

If we evaluate $x=\frac{4*(2+e)}{e-2}$ in the original equation:

$log(2*((\frac{4e+8}{e-2})^2-16))-log((\frac{4e+8}{e-2}-4)^2)=1$

Which is correct, therefore the solution is:

$x=\frac{4*(2+e)}{e-2}$

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4 years ago

How to solve 6x-3=7x-11

VladimirAG [237]

Hello there.

How to solve 6x-3=7x-11
6x−3=7x−11
6x−3−7x=7x−11−7x−x−3=−11
−x−3+3=−11+3−x=−8
−x/−1=−8/−1x=8
Answer: 8

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3 years ago

2x+y=5 , 3x+2y=8 solve using cross multiplication​

2x+y=5 , 3x+2y=8 solve using cross multiplication