Convert without rounding: 5/8 into a decimal = ?

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

LiRa [457]

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:

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

8 0

3 years ago

Consider the following pair of equations:

frozen [14]

X+4=y=-2x-2
x+4=-2x-2
add 2x to both side
3x+4=-2
minus 4 both sides
3x=-6
divide 3
x=-2

sub back
y=x+4
y=-2+4
y=2

(x,y)
(-2,2)

3 0

3 years ago

X is less than or equal to 24.

GREYUIT [131]

Answer:

yes

Step-by-step explanation:

x isnt a number

6 0

3 years ago

Read 2 more answers

According to the most recent census, the average total yearly expenses of households in Wake County is $45,900. It is also known

Anni [7]

Answer:

a. The sampling distribution of the sample mean will have a smaller standard deviation than the population.

b. The sampling distribution of the sample mean will have a different standard deviation than the population.

c. The shape of the sampling distribution of the sample mean will be skewed right.

Step-by-step explanation:

4 0

3 years ago

An arts academy requires there to be 3 teachers for every 75 students and 6 tutors for every 72 students. How many tutors does t

suter [353]

5 teachers and 10 tutors because we can make a proportion:

3/75=x/120, and when you cross multiply and solve for x you will get 4.8, but there can't be 4.8 teachers so we can say 5 teachers (round). Do the same for tutors: 6/72=x/120, x would equal 10.

Hope this helps!

4 0

3 years ago

Read 2 more answers