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3 years ago

How do you solve linear equations with substitutions?

Mathematics

1 answer:

Nostrana [21]3 years ago

5 0

Answer:

The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.

Step-by-step explanation:

Solve the following system by substitution.

2x – 3y = –2

4x + y = 24

The idea here is to solve one of the equations for one of the variables, and plug this into the other equation. It does not matter which equation or which variable you pick. There is no right or wrong choice; the answer will be the same, regardless. But — some choices may be better than others.

For instance, in this case, can you see that it would probably be simplest to solve the second equation for "y =", since there is already a y floating around loose in the middle there? I could solve the first equation for either variable, but I'd get fractions, and solving the second equation for x would also give me fractions. It wouldn't be "wrong" to make a different choice, but it would probably be more difficult. Being lazy, I'll solve the second equation for y:

4x + y = 24

y = –4x + 24

Now I'll plug this in ("substitute it") for "y" in the first equation, and solve for x:

2x – 3(–4x + 24) = –2

2x + 12x – 72 = –2

14x = 70

x = 5

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Lakshmi donates 20% of her income to charity.

Vlad1618 [11]

Answer:1/5

Step-by-step explanation:

Just put 20 over 100 and simplify. The answer is 1/5.

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3 years ago

Use slope-intercept form, y = mx + b to find the equation of the line that passes through the points (−6, 1) and (3, 4).

Vilka [71]

To find this, you have to find your slope with the given x and y values first. Use the equation Y2-Y1/X2-X1 for finding the slope.
4-1/3- -6
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Now you know your slope is 1/3, and you can basically assume your third answer listed is correct since none of the other ones contain a positive 1/3 but I will explain how to continue for future use. Next you can use one set of x and y values to plug into the equation y=mx+b, and plug in 1/3 for m as well.

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Now you have your y intercept and your slope, so you can make your equation.

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4 years ago

Read 2 more answers

In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?

telo118 [61]

The ratio of the sine of

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3 years ago

Find x <br> 2 ^30 divided by 8^9= 2x

Zarrin [17]

$\huge\text{Hey there!}$

$\mathsf{\dfrac{2^{30}}{8^9}=2x}$

$\mathsf{2^{30}}\\\mathsf{= \bf 1,073,741,824}\\\\\mathsf{8^9}\\\mathsf{= \bf 134,217,728}$

$\mathsf{\rightarrow \dfrac{1,073,741,824}{134,217,728}= 2x}\\\\\\\mathsf{\dfrac{1,073,741,824}{134,217,728}= \bf 8}\\\\\\\mathsf{\rightarrow \ 8 = 2x}\\\\\\\\\large\textsf{TURN\ the\ EQUATION\ around}\\\\\\\mathsf{\rightarrow\ 2x = 8}\\\\\\\large\textsf{DIVIDE 2 to BOTH SIDES}\\\\\\\mathsf{\dfrac{2x}{2}=\dfrac{8}{2}}\\\\\\\large\textsf{CANCEL out: }\mathsf{\dfrac{2}{2}}\large\textsf{ because it gives you 1}\\\\\\\large\textsf{KEEP: }\mathsf{\dfrac{8}{2}}\large\textsf{ because it gives you the answer of x}$

$\mathsf{x = \dfrac{8}{2}}\\\\\\\mathsf{x = 8\div 2}\\\\\\\mathsf{x = \bf 4}\\\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 4}}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

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3 years ago

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Greg have 24 more stickers than Wayne and Ronald have twice as much stickers than Wayne together they have 124 stick how much ea

lukranit [14]

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3 years ago