All categories

3 years ago

Solve the system by substitution: y = -3x + 10 y=-3x + 4 Please show the steps!

Mathematics

1 answer:

sergiy2304 [10]3 years ago

5 0

Answer:

x=1, y=7

Step-by-step explanation:

y = -3x + 10 - first equation

y=-3x + 4 - second equation

rearrange the expression to

-3x-y= -10

3x-y= -4

pick an equation and simplify; lets pick the second equation

3x-y= -4

$\frac{3x}{3} = \frac{-4+y}{3}$

divide 3 by both sides

x= $\frac{-4+y}{3}$ - third equation

substitute the value of x into an equation; lets pick the first equation

-3x-y= -10

-3 $(\frac{-4+y}{3})$ - y = -10

simplify. -3 cancels 3 so we are left with

-1(-4+y)-y = -10

simplify

4-y-y= -10

4-2y= -10

subtract 4 from both sides

-2y= -10-4

-2y= -14

divide -2 by both sides

y=7

substitute the value of y, (y=7) in an equation, we are using the second equation

3x-y= -4

3x-7= -4

3x = -4+7

3x= 3

divide 3 by both sides

x=1

so the answer is x=1, y=7

You might be interested in

The measurenicnt of the circumference of a circle is found to be 56 centimeters. The possible error in measuring the circumferen

BartSMP [9]

Answer:

(a) Approximate the percent error in computing the area of the circle: 4.5%

(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the area cannot exceed 3%: 0.6 cm

Step-by-step explanation:

(a)

First we need to calculate the radius from the circumference:

$c=2\pi r\\r=\frac{c}{2\pi } \\c=8.9 cm$

I leave only one decimal as we need to keep significative figures

Now we proceed to calculate the error for the radius:

$\Delta r=\frac{dt}{dc} \Delta c\\\\\frac{dt}{dc} = \frac{1}{2 \pi } \\\\\Delta r=\frac{1}{2 \pi } (1.2)\\\\\Delta r= 0.2 cm$

$r = 8.9 \pm 0.2 cm$

Again only one decimal because the significative figures

Now that we have the radius, we can calculate the area and the error:

$A=\pi r^{2}\\A=249 cm^{2}$

Then we calculate the error:

$\Delta A= (\frac{dA}{dr} ) \Delta r\\\\\Delta A= 2\pi r \Delta r\\\\\Delta A= 11.2 cm^{2}$

$A=249 \pm 11.2 cm^{2}$

Now we proceed to calculate the percent error:

$\%e =\frac{\Delta A}{A} *100\\\\\%e =\frac{11.2}{249} *100\\\\\%e =4.5\%$

(b)

With the previous values and equations, now we set our error in 3%, so we just go back changing the values:

$\%e =\frac{\Delta A}{A} *100\\\\3\%=\frac{\Delta A}{249} *100\\\\\Delta A =7.5 cm^{2}$

Now we calculate the error for the radius:

$\Delta r= \frac{\Delta A}{2 \pi r}\\\\\Delta r= \frac{7.5}{2 \pi 8.9}\\\\\Delta r= 0.1 cm$

Now we proceed with the error for the circumference:

$\Delta c= \frac{\Delta r}{\frac{1}{2\pi }} = 2\pi \Delta r\\\\\Delta c= 2\pi 0.1\\\\\Delta c= 0.6 cm$

5 0

3 years ago

Which problem solving strategy would be best to solve this problem? How many different ways can you give change for 45 cents?

hodyreva [135]

I think A since working backwards and looking for a pattern wouldn't help, maybe C but im not sure

6 0

3 years ago

Read 2 more answers

A boat travels upstream for 48 miles in 3 hours and returns in 2 hours traveling downstream in a river. What is the rate of the

alekssr [168]

Answer:

20 mph and 4 mph

Step-by-step explanation:

GIVEN: A boat travels upstream for $48$ miles in $3$ hours and returns in $2$ hours traveling downstream in a river.

TO FIND: What is the rate of the boat in still water and the rate of the current.

SOLUTION:

Let the speed of boat in still water be $s$ and speed of current be $a$ .

$\therefore$ speed of water in upstream $=s+a$

speed of water in downstream $=s-a$

As $speed=\frac{distance}{time}$

$s+a=\frac{48}{3}=16$

$s-a=\frac{48}{2}=24$

Solving both we get

$s=20\text{ mph}$

$a=4\text{ mph}$

Hence speed of boat in still water and rate of current is 20mph and 4mph respectively.

3 0

3 years ago

BEST ANSWER EARNS BRAINLIEST!

Lady bird [3.3K]

Please mark brainliest 3 more to rankup.

so is how I would solve this is one corner at a time. Since these are all triangles you will solve the area of a corner and divide it by 2. Then you will have the area of a corner.

(7.5 x 5) /2= 18.75
(7.5 x 14) /2=52.5
Mirror this on the other side because they are the same on the other side and then add them all together

(18.75 x 2) + (52.5 x 2) = 142.5

Answer is A
142.5

3 0

3 years ago

The pearson correlation coefficient measures the strength of the linear association between two variables, x and y, regardless o

Vlada [557]

That is correct do I get the points?

7 0

3 years ago