All categories

2 years ago

How do you solve linear equations with substitutions?

Mathematics

1 answer:

Nostrana [21]2 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

You might be interested in

600+600-200 Giving Brainliest

Mila [183]

Equation Answer is 1,000!

7 0

3 years ago

Read 2 more answers

Anyone know how to answer this question

mart [117]

9514 1404 393

Answer:

(x +6)^2 +(y -10)^2 = 225

Step-by-step explanation:

The standard form equation for a circle is ...

(x -h)^2 + (y -k)^2 = r^2

where the center is (h, k) and the radius is r.

The center of a circle is the midpoint of any diameter. The midpoint between two points is the average of their coordinates.

((-15, -2) +(3, 22))/2 = (-15+3, -2+22)/2 = (-6, 10)

The radius can be found using the distance formula, or by simply putting one of the given points in the equation for the circle to see what the constant (r^2) needs to be.

(x -(-6))^2 +(y -10)^2 = (-15-(-6))^2 +(-2-10)^2

(x +6)^2 +(y -10)^2 = 81 +144 = 225

The equation of the circle is ...

(x +6)^2 +(y -10)^2 = 225

5 0

3 years ago

What kind of taxes are likely to pay for universities and police? a. local taxes b. state taxes c. federal taxes d. income taxes

shusha [124]

The best choice is B, state taxes !

7 0

3 years ago

Read 2 more answers

Ap calc multiple choice question; attached below please explain how, please!

anygoal [31]

Answer:

C. $\frac{f(b)-f(1)}{b-1}=20$

General Formulas and Concepts:

Calculus

Mean Value Theorem (MVT) - If f is continuous on interval [a, b], then there is a c∈[a, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

MVT is also Average Value

Step-by-step explanation:

Step 1: Define

$f(x)=e^{2x}$

f'(c) = 20

Interval [1, b]

Step 2: Check/Identify

Function [1, b] is continuous.

Derivative [1, b] is continuous.

∴ There exists a c∈[1, b] such that $f'(c)=\frac{f(b)-f(a)}{b-a}$

Step 3: Mean Value Theorem

Substitute: $20=\frac{ f(b)-f(1)}{b-1}$
Rewrite: $\frac{ f(b)-f(1)}{b-1}=20$

And we have our final answer!

5 0

2 years ago

At wild thing zoo, you can rent a motorized cart to tour grounds for a $3 initial charge and $7 per hour. at safari zoo, you can

makvit [3.9K]

When setting up the equation you have the initial fee and the hourly fee. The hourly fee is what must be multiplied by the number of hours which is our unknown

6 0

3 years ago