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3 years ago

13. Find the solution to the following system of equations using any method: 4x - y = 3 -4x + y = -3

Mathematics

1 answer:

forsale [732]3 years ago

3 0

Start by writing out the system of equations.

4x - y = 3
-4x + y = -3

The easiest way to solve this system of equations is the elimination method. This is because both equations contain opposites of each other that you can cancel out.

Add the system of equations together. After adding, everything cancels out. 4x + (-4x) = 0 ; -y + y = 0 ; 3 + (-3) = 0.

You are left with the equation of 0 = 0. Since this is a TRUE statement, this means that there are infinitely many solutions to this system of equations.

If you were left with a false statement, for example 4 = 0, then the answer would be "no solution".

Another way to solve this system of equations is by the substitution method. This method works best if you are given a system of equations with one variable clearly defined.

For example, the system of equations could be:

4x - y = 3
y = 3x + 4

y is equal to 3x + 4, so you could easily substitute y into the first equation. The elimination method wouldn't be the best choice because the system of equations are in the standard form Ax + By = C.

Generally any system of equations in the standard form are easier to solve using the elimination method. Hope this helped, good luck!

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Jada, Lin, and Elena are saving money for a trip. Together they saved $120. Jada saved $20 less than Lin. Lin saved 3 times as m

defon

Step-by-step explanation:

This is a word problem that we must translate to mathematical expression before we can solve.

let the individual saving be the first letters of the names

Jada= J

Lin= L

Elena= E

1. Jada saved $20 less than Lin

J=L-20

2. Lin saved 3 times as much money as Elena

L= 3E

3. Hence Elena saved

Together they saved $120.

hence

(L-20)+3E+E= 120

L-20+3E+E= 120

collecting like terms we hav

L+4E=120+20

L+4E= 140

but we know that L= 3E

3E+4E= 140

7E= 140

divide both sides by 7 we have

E= 140/7

E= $20

This means Elena saves $70

also L= 3E

L= 3*20

L= $60

this means that Lean saved $60

also J=L-20

J= 60-20

J= $40

This means that Jada saved $40

6 0

3 years ago

What is the area of a rectangle with sides measuring 2x+3 and 3x-1 feet

Ber [7]

Here is your answer

4 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=12%5Ctimes%2012%5Ctimes%2011" id="TexFormula1" title="12\times 12\times 11" alt="12\times 12\t

vekshin1

12 x 12 x 11
12 x 12 = 144
144 x 11 = 1584

the answer is 1584 ! hope that helps :)

5 0

3 years ago

Sam bought 15 pies and 7 slices of cake for $55.25. If each pie cost 2/5 as much as a slice of cake, what was the total cost of

romanna [79]

Answer: $10.20

Step-by-step explanation:

Let's first collect the information from the word problem.

Bought 15 pies and 7 cake slices

Total cost was $55.22.
Pies cost $\frac{2}{5}$ as much as a slice of cake

<h3><em>We need to solve for:</em></h3>

Total cost of 1 pie and 2 cake slices

1. Create an equation/expression:

To solve the problem, we need to find the price of a pie and cake slice.

Using the information gathered, the equation is:

$55.25 = 7x+15(\frac{2}{5} x)$

<em>x = the cost of the slice of cake.</em>

<em />

2. Simplify/Solve

$55.25 = 7x+15(\frac{2}{5}x)\\55.25 = 7x+15*\frac{2}{5}*x\\55.25 = 7x+6x\\55.25 = 13x\\4.25 = x$

Great! we have the price of a slice of cake. ($4.25)

Remember that the pie is $\frac{2}{5}$ of a slice of cake, so now find the price of the pies.

Pie = $\frac{2}{5} 4.25$

Pie = $1.70

Awesome! We know a slice of cake costs $4.25 and a slice of pie costs $1.70.

3. Check your work!

<em>Check to make sure the math is done correctly!</em>

$55.25=7(4.25)+15(1.70) \\55.25=29.75+25.50\\55.25=55.25$

Good! It is verified that our calculations are correct.

4. Solve!

1 pie and 2 cakes cost: $1.70+2(4.25)$

$10.20 is our final answer!

Hope this helped!~~ -Astro

7 0

4 years ago

I am a multiple of 12 . i am between 40 and 50 . who could i be

DedPeter [7]

Answer:

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers