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3 years ago

What is the solution to the system of equations below? -4x+6y=-18 and y=-2x+21

Mathematics

1 answer:

Verdich [7]3 years ago

3 0

Answer:

x=9 and y=3

Step-by-step explanation:

Let's solve your system by substitution.

−4x+6y=−18 and y=−2x+21

Rewrite equations:

y=−2x+21;−4x+6y=−18

Step: Solve y=−2x+21for y:

y=−2x+21

Step: Substitute−2x+21foryin−4x+6y=−18:

−4x+6y=−18

−4x+6(−2x+21)=−18

−16x+126=−18(Simplify both sides of the equation)

−16x+126+−126=−18+−126(Add -126 to both sides)

−16x=−144

−16x

−16

−144

−16

(Divide both sides by -16)

x=9

Step: Substitute9forxiny=−2x+21:

y=−2x+21

y=(−2)(9)+21

y=3(Simplify both sides of the equation)

Answer:

x=9 and y=3

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Explanation:

Draw out a number line. Mark 75, 100 and 125 on the number line as points A, B, and C in that order. Don't worry about the spacing.

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3 years ago

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2 years ago

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2 years ago

The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would

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Answer:

A: True

B, C and D: False

Step-by-step explanation:

We have a total sales tax for Alabama that is:

$T_A=4.225+1.375+3=8.6$

The total sales tax for Florida is:

$T_F=6.5+1+1.625=9.125$

The total sales tax is greater in Florida than in Alabama.

A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE

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$1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8$

B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)

C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)

The amount of sales tax in Alabama is:

$ST_A=1500\cdot T_A=1500\cdot 0.086=129$

D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).

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2 years ago