Ask question

Ask question

All categories

2 years ago

10

How many solutions does the system have?

1 answer:

kykrilka [37]2 years ago

6 0

Answer: a

Infinitely many

Step-by-step explanation:

Solve by substitution:

1) Solve $y=2x+1$ for $y$ :

$y=2x+1$

2) Substitute $2x+1$ for $y$ in $-4x+2y=2$ :

$-4x+2y=2$

$-4x+2(2x-1)=2$

3) Simplify both sides of the equation:

$2=2$

4) Add -2 to both sides of the equation:

$2+-2=2+-2$

5) Simplify both sides of the equation:

$0=0$

Therefore, there are infinitely many solutions.

Solve by elimination:

You cannot solve this system by elimination

Solve by graphing:

The $2$ equations are on top of each other, therefore, the system of equations has infinitely many solutions.

You might be interested in

Solve the following system

scZoUnD [109]

Answer:

{x = -4 , y = 2 , z = 1

Step-by-step explanation:

Solve the following system:

{-2 x + y + 2 z = 12 | (equation 1)

2 x - 4 y + z = -15 | (equation 2)

y + 4 z = 6 | (equation 3)

Add equation 1 to equation 2:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - 3 y + 3 z = -3 | (equation 2)

0 x+y + 4 z = 6 | (equation 3)

Divide equation 2 by 3:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+y + 4 z = 6 | (equation 3)

Add equation 2 to equation 3:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+0 y+5 z = 5 | (equation 3)

Divide equation 3 by 5:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y + z = -1 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 3 from equation 2:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x - y+0 z = -2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Multiply equation 2 by -1:

{-(2 x) + y + 2 z = 12 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract equation 2 from equation 1:

{-(2 x) + 0 y+2 z = 10 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Subtract 2 × (equation 3) from equation 1:

{-(2 x)+0 y+0 z = 8 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Divide equation 1 by -2:

{x+0 y+0 z = -4 | (equation 1)

0 x+y+0 z = 2 | (equation 2)

0 x+0 y+z = 1 | (equation 3)

Collect results:

Answer: {x = -4 , y = 2 , z = 1

4 0

3 years ago

The circumference of ruby's old swimming pool is 47.1 feet. Her new swimming pool has a diameter of 21 feet. How much larger is

Alla [95]

The new pool is 18.84 feet larger in circumference than the old one.

<u>Explanation:</u>

Given:

Circumference of the pool = 47.1 feet

Diameter of the new pool, d = 21 feet

radius, r = 21/2 feet

Circumference of the new pool = ?

We know:

Circumference = 2πr

where,

r is the radius

On substituting the value:

C = $2 X 3.14 X \frac{21}{2}$

C = 65.94 feet

The difference in circumference of the two pools = 65.94 - 47.1 feet

= 18.84 feet

Therefore, the new pool is 18.84 feet larger in circumference than the old one.

6 0

3 years ago

Which best describes a scalene triangle?

FinnZ [79.3K]

Answer:

All three sides of the triangle are different lengths.

Step-by-step explanation:

hope this helps :)

6 0

3 years ago

Read 2 more answers

Relative risk is an ideal form of measurement for a retrospective cohort study design because it allows researchers to recruit b

kolezko [41]

This indicates that the individuals taking vitamin C were 53% less likely to catch a cold and that taking vitamin C has a protective effect, making them less likely to catch a cold.

This is further explained below.

<h3>What is vitamin C?</h3>

Generally, Vitamin C, which is also known as ascorbic acid, is an essential nutrient for the expansion, maturation, and maintenance of all of the body's tissues. It plays an important role in the synthesis of collagen, the absorption of iron, the appropriate functioning of the immune system, the healing of wounds, and the preservation of cartilage, bones, and teeth.

In conclusion, This suggests that those persons who took vitamin C were 53% less likely to develop a cold and that taking vitamin C has a protective impact, making them less likely to catch a cold.

Additionally, this implies that taking vitamin C makes one less likely to catch a cold.

Read more about vitamin C

brainly.com/question/15080220

#SPJ1

CQ

Researchers have conducted a study and determined that the relative risk for developing a cold for individuals taking vitamin C is 0.47 when compared to the number of participants in the study who developed a cold while not taking vitamin C. This is an indication of which of the following?

6 0

1 year ago

8. The measures of two angles in an isosceles triangle are shown in the diagram.

mote1985 [20]

Answer:

A

Step-by-step explanation:

Because 45 + 2x = 180 divide it by 2 gives 4

8 0

3 years ago