All categories

3 years ago

Match the systems of linear equations with their solutions.

Mathematics

1 answer:

OleMash [197]3 years ago

6 0

Answer:

The solutions of linear equations in the procedure

Step-by-step explanation:

Part 1) we have

x+y=-1 ----> equation A

-6x+2y=14 ----> equation B

Solve the system by elimination

Multiply the equation A by 6 both sides

6*(x+y)=-1*6

6x+6y=-6 -----> equation C

Adds equation C and equation B

6x+6y=-6

-6x+2y=14

-------------------

6y+2y=-6+14

8y=8

y=1

Find the value of x

substitute in the equation A

x+y=-1 ------> x+1=-1 ------> x=-2

The solution is the point (-2,1)

Part 2) we have

-4x+y=-9 -----> equation A

5x+2y=3 ------> equation B

Solve the system by elimination

Multiply the equation A by -2 both sides

-2*(-4x+y)=-9*(-2)

8x-2y=18 ------> equation C

Adds equation B and equation C

5x+2y=3

8x-2y=18

----------------

5x+8x=3+18

13x=21

x=21/13

Find the value of y

substitute in the equation A

-4x+y=-9 ------> -4(21/13)+y=-9 ----> y=-9+84/13 -----> y=-33/13

The solution is the point (21/13,-33/13)

Part 3) we have

-x+2y=4 ------> equation A

-3x+6y=11 -----> equation B

Multiply the equation A by 3 both sides

3*(-x+2y)=4*3 ------> -3x+6y=12

Line A and Line B are parallel lines with different y-intercept

therefore

The system has no solution

Part 4) we have

x-2y=-5 -----> equation A

5x+3y=27 ----> equation B

Solve the system by elimination

Multiply the equation A by -5 both sides

-5*(x-2y)=-5*(-5)

-5x+10y=25 -----> equation C

Adds equation B and equation C

5x+3y=27

-5x+10y=25

-------------------

3y+10y=27+25

13y=52

y=4

Find the value of x

Substitute in the equation A

x-2y=-5 -----> x-2(4)=-5 -----> x=-5+8 ------> x=3

The solution is the point (3,4)

Part 5) we have

6x+3y=-6 ------> equation A

2x+y=-2 ------> equation B

Multiply the equation B by 3 both sides

3*(2x+y)=-2*3

6x+3y=6

Line A and Line B is the same line

therefore

The system has infinite solutions

Part 6) we have

-7x+y=1 ------> equation A

14x-7y=28 -----> equation B

Solve the system by elimination

Multiply the equation A by 7 both sides

7*(-7x+y)=1*7

-49x+7y=7 -----> equation C

Adds equation B and equation C

14x-7y=28

-49x+7y=7

------------------

14x-49x=28+7

-35x=35

x=-1

Find the value of y

substitute in the equation A

-7x+y=1 -----> -7(-1)+y=1 ----> y=1-7 ----> y=-6

The solution is the point (-1,-6)

You might be interested in

URGENT,PLEASE HELP ME !!!!!!!!!!!!!!!

kakasveta [241]

Answer: The last one

Step-by-step explanation:

I think this because the graph starts from H the number of hours studied and when u add the numbers and divide them up which gives you the equation 65 + 50 . Any questions please text me. Have a nice day.

8 0

2 years ago

Can someone please help i really need to ace this <br><br> x = ___ degrees

lord [1]

Answer:pretty sure its 10 degrees

Step-by-step explanation:

all tris add up to 180, and this one is a right angle so you know you have 90 deg, 80 degrees. 90+80=170; 180-170=10

6 0

2 years ago

The functions g and h are given by g(x) = x + 1 and h(x) = x²

Delvig [45]

Answer:

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

Step-by-step explanation:

To find h(g(x)) substitute x = g(x) into h(x) , that is

h(g(x))

= h(x + 1)

= (x + 1)²

= x² + 2x + 1

For h(g(x)) = 3x² + x - 5 , then

3x² + x - 5 = x² + 2x + 1 ← subtract x² + 2x + 1 from both sides

2x² - x - 6 = 0 ← in standard form

(2x + 3)(x - 2) = 0 ← in factored form

Equate each factor to zero and solve for x

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

x - 2 = 0 ⇒ x = 2

5 0

2 years ago

Please help with a math problem :/ Please show steps...<br><br> x^2 -13x = -36

Marianna [84]

X^2 - 13 x = -36
add 36 to both sides

x^2 - 13x +36 = 0
figure out the factor
(x-4)(x-9) = 0
so (x-4) or (x-9) equals 0
so solution is
x-4=0 add 4 to both sides and get x = 4
x-9=0 add 9 to both sides and get x=9
x={ 4, 9}

4 0

3 years ago

An expression is shown below

Leno4ka [110]

Answer:

B) It is irrational and equal to $= 4\sqrt{2}$

Step-by-step explanation:

The expression, $\sqrt{18} + \sqrt{2}$ , is an irrational expression because it contains two irrational numbers, $\sqrt{18}$ and $\sqrt{2}$ . Both number are not perfect square. there is no whole number that would be squared that will give you 18 nor 2.

The expression can be equals the following:

$\sqrt{18} + \sqrt{2}$

$= \sqrt{9*2} + \sqrt{2}$

$= \sqrt{9}*\sqrt{2} + \sqrt{2}$

$= 3\sqrt{2} + \sqrt{2}$

$= 4\sqrt{2}$

4 0

2 years ago