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3 years ago

3g+h=18 2g+3h=26 what is h and what is g

Mathematics

2 answers:

Damm [24]3 years ago

7 0

Answer:

g = 4; h = g

Step-by-step explanation:

When solving an equation with two variables, the goal is to isolate at least one of the variables so that you can plug it in to the equation to get the other. There are multiple ways to solve this so I'll just be giving one.

3g + h = 18

2g + 3h = 26

In these two equations, I notice that if I multiply the first equation by 3, the two equations will have the same values of h, so I'd be able to isolate g:

9g + 3h = 54

2g + 3h = 26

Now, subtract the second equation from the first to isolate g:

9g + 3h = 54

-2g + 3h = 26

= 7g = 28

= g = 4

Now that we have solved for g, we can plug it into either of the equations and solve for h:

2(4) + 3h = 26

= 8 + 3h = 26

= 3h = 18

= h = 6

And in conclusion, g = 4 and h = 6.

NeTakaya3 years ago

4 0

Answer:

g=4 h=6

Step-by-step explanation:

3g +h = 18 (Equation 1)

2g+3h=26 (Equation 2)

From equation 1

3g+ h =18

h= 18-3g (equation 3)

substitute equation 3 into equation 2

2g+3h= 26

2g+ 3(18-3g)= 26

2g+3×18+3(-3g)=26

2g+54-9g=26

9g-2g= 54-26

7g=28

7g÷7 = 28÷7

g= 4

substitute g into equation 1

3g+h=18

3(4)+ h= 18

12+h= 18

h=18-12

h= 6

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3 years ago

7+3√5/3+√5 - 7-3√5/3-√5 = a + b√5

daser333 [38]

<h3>Given:-</h3>

$\\ \sf \implies\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } = a + \sqrt{5} b \\$

The value of a and b

<h3>Solution:-</h3>

$\\ \sf \implies\frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } = a + \sqrt{5} b \\$

$\\ \sf \implies\frac{( \: 7 + 3 \sqrt{5} \: \: ( 3 - \sqrt{5}) \: \: - 7 - 3 \sqrt{5} \: \: ( 3 + \sqrt{5}) \: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{( \: 21 - 7 \sqrt{5} \: + 9 \sqrt{5} - 15) \: \: - ( \: 21 + 7 \sqrt{5} \: - 9 \sqrt{5} + 15)\: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{( \: 6 + 2 \sqrt{5} ) \: \: - ( \: 6 - 2 \sqrt{5} )\: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 6 + 2 \sqrt{5} \: \: - \: \: 6 - 2 \sqrt{5} \: }{(3 + \sqrt{5}) \: \:(3 + \sqrt{5}) } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 4 \sqrt{5} \: \: }{3 {}^{2} - {\sqrt{5} }^{2} } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 4 \sqrt{5} \: \: }{ \: \: \: \: 9 - 5 \: \: \: } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: 4 \sqrt{5} \: \: }{ \: \: \: \: 4 \: \: \: } = a + \sqrt{5} \: b\\$

$\\ \sf \implies\frac{\: \cancel{4 } \sqrt{5} \: \: }{ \: \: \: \: \cancel{4 }\: \: \: } = a + \sqrt{5} \: b\\$

$\\ \sf \implies \: \sqrt{5} = a + \sqrt{5} \: b\\$

we can also write it as ;

$\\ \sf \implies \: 0 + \sqrt{5} = a + \sqrt{5} \: b\\$

★<u> </u><u>Henceforth, the value of a and b are</u> :

→ a = 0

→ b = 1

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