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3 years ago

3x+4y=29 6x+5y=43 Solve through elimination

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

6 0

Answer:

Let's solve your system by elimination.

3x+4y=29;6x+5y=43

Multiply the first equation by -2,and multiply the second equation by 1.

−2(3x+4y=29)

1(6x+5y=43)

Becomes:

−6x−8y=−58

6x+5y=43

Add these equations to eliminate x:

−3y=−15

Then solve−3y=−15for y:

−3y=−15

−3y −3 = −15

−3

(Divide both sides by -3)

y=5

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

3x+4y=29

Substitute5foryin3x+4y=29:

3x+(4)(5)=29

3x+20=29(Simplify both sides of the equation)

3x+20+−20=29+−20(Add -20 to both sides)

3x=9

3x 3 = 9

(Divide both sides by 3)

x=3

Answer:

x=3 and y=5

Step-by-step explanation:

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Which methods correctly solve for the variable s in the equation -2 - 5s =9?

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2 years ago

Read 2 more answers

1011+111 in binary form

Ann [662]

Answer:

10010

Step-by-step explanation:

$1011=1(2)^3+0(2)^2+1(2)^1+1(2)^0$

$111=1(2)^2+1(2)^1+1(2)^0$

So $1011+111$ gives us:

$1(2)^3+0(2)^2+1(2)^1+1(2)^0$

$+$

$1(2)^2+1(2)^1+1(2)^0$

-----------------------------------------------------

Combine like terms:

$1(2)^3+(0+1)(2)^2+(1+1)(2)^1+(1+1)(2)^0$

$1(2)^3+1(2)^2+(2)(2)^1+(2)(2)^0$

We aren't allowed to have a coefficient bigger than 1.

I'm going to replace $2^0$ with 1 and $2$ with $(2)^1$ :

$1(2)^3+1(2)^2+(2)^2+(2)^1(1)$

I want a $2^0$ number:

$1(2)^3+1(2)^2+1(2)^2+1(2)^1+0(2)^0$

Combine like terms:

$1(2)^3+2(2)^2+1(2)^1+0(2)^0$

$2(2)^2=2^3$ :

$1(2)^3+2^3+1(2)^1+0(2)^0$

Combine like terms:

$2(2)^3+1(2)^1+0(2)^0$

We can rewrite the first term by law of exponents:

$2^4+1(2)^1+0(2)^0$

$1(2)^4+1(2)^1+0(2)^0$

So the binary form is:

$10010$

Maybe you like this way more:

Keep in mind 1+1=10 and that 1+1+1=11:

Setup:

1 0 1 1

+ 1 1 1

------------------------------

(1) (1) (1)

1 0 1 1

+ 1 1 1

------------------------------

1 0 0 1 0

I had to do some carry over with my 1+1=10 and 1+1+1=11.

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3 years ago

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exis [7]

Answer:

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2x - 4 = 5 (2) subtract 5

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