1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lana [24]
3 years ago
11

Code. -3x + 4y = -8 8x - y = 16 Solving systems by substitution

Mathematics
1 answer:
LiRa [457]3 years ago
8 0

Answer:

The solution to the system of equations is \displaystyle \big(\frac{56}{29}, -\frac{16}{29}\big).

Step-by-step explanation:

We are given a system of equations:

\displaystyle \left \{ {{-3x+4y=-8} \atop {8x-y=16}} \right.

  • We need to solve these by substitution, so we need to solve one equation for a variable and then substitute the value of that variable into the other equation.
  • After doing this and solving for the opposite variable, we need to insert this into the original equation and solve for the initial variable.
  • Therefore, to solve one of the equations, we will solve it to put it in slope-intercept form and solve for y. The easier equation to work with is equation two.

\displaystyle 8x - y = 16\\\\-y = -8x + 16\\\\\frac{-y}{-1}=\frac{-8x+16}{-1}\\\\y = 8x - 16

Now, we've solved for y. So, we can substitute this into either equation and solve for x.

\displaystyle -3x + 4(8x -16)=-8\\\\-3x + 32x - 64 = -8\\\\29x - 64 = -8\\\\29x = 56\\\\\frac{29x}{29}=\frac{56}{29}\\\\x = \frac{56}{29}

Now, we substitute our value for x into one of the original equations and solve for y.

\displaystyle 8\big(\frac{56}{29}\big)-y=16\\\\-y = 16 - 8\big(\frac{56}{29}\big)\\\\-y=\frac{16}{29}\\\\\frac{-y}{-1}=\frac{\frac{16}{29}}{-1}\\\\y = -\frac{16}{29}

Therefore, the solution to our system of equations is:

  • \displaystyle \big(\frac{56}{29}, -\frac{16}{29}\big)

You might be interested in
A=e(b-c)-d<br><br><br> B=6, c=3,d=-4, e=-2<br><br> Find the value please
MissTica

Answer:

A=e(b-c)-d

A=-2(6-3)-4

A=-12+6-4

A=-6-4

A=-10

3 0
2 years ago
Write 25/22 as a decimal and round it to the nearest hundredth
MrRissso [65]

Answer: 1.14

Step-by-step explanation:

25/22 = 1.1363

7 0
3 years ago
The slopes of perpendicular line segments are start fraction one over three end fraction and start fraction d over five end frac
Brums [2.3K]

Answer:

d = -15

Step-by-step explanation:

The slopes of perpendicular lines have a product of -1.

1/3·d/5 = -1

d/15 = -1 . . . . simplify

d = -15 . . . . . multiply by 15

8 0
3 years ago
Factor then solve.<br> ​ 3x2+14x+8=0
tangare [24]

Answer:

x = - 4, x = - \frac{2}{3}

Step-by-step explanation:

Given

3x² + 14x + 8 = 0

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 + 8 = 24 and sum = + 14

The factors are + 12 and + 2

Use these factors to split the x- term

3x² + 12x + 2x + 8 = 0 ( factor the first/second and third/fourth terms )

3x(x + 4) + 2(x + 4) = 0 ← factor out (x + 4) from each term

(x + 4)(3x + 2) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

3x + 2 = 0 ⇒ 3x = - 2 ⇒ x = - \frac{2}{3}

4 0
3 years ago
In an elementary school, 25% of the 252 students ride a bus to school each day. How many students ride the bus?
Lady bird [3.3K]

Answer:

63

Step-by-step explanation:

7 0
4 years ago
Other questions:
  • What is the coefficient of the term x7y in the expansion of (x + y)8?
    14·1 answer
  • Convert 250 ounces into quarts
    7·2 answers
  • a certain medicine is given in an amount proportional to a patient's body weight supposed patient weighing 104 lb requires 130 m
    13·1 answer
  • Zipora wants to construct a triangle that has the following angle measures: 50°, 75°, and 55°. How many triangles can she make?
    8·1 answer
  • Tell whether x and y show direct variation 5y=x
    13·1 answer
  • Find an equation of the circle that has center (-1,1 ) and passes through (1,-6)
    14·1 answer
  • Mr. Norris buys a boat for $125,000. He has to pay a 5% tax on his purchase of the boat. How much money is the tax?
    9·1 answer
  • 2 x - 3+ 1 x6 is equal to?<br><br> A. - 48<br> B. - 1<br> C.0<br> D. 1
    15·1 answer
  • PLEASE HELP IF POSSIBLE :)
    7·1 answer
  • HELP ME RN PLEASE!!!!!!!!!!!!!!!!!!!!!!
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!