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
Aleksandr-060686 [28]
3 years ago
14

Find the intersection point between the lines of equations:x+y-2=0 and 3x-y+4=0 ​

Mathematics
1 answer:
inn [45]3 years ago
8 0

Answer:

(-0.5,2.5)

Step-by-step explanation:

The given equations are ,

\implies x + y - 2 = 0

\implies 3x -  y +4 = 0

The point of intersection will be the solution of the given system of equations. Adding both , y will get cancelled . So that ,

\implies 4x +2 = 0

Now solve for x , we have ,

\implies 4x = -2 \\\\\implies x =\dfrac{-2}{4}\\\\\implies x = -0.5

Now put this value in any equation and solve out for y , we have ,

\implies -0.5 + y - 2 = 0 \\\\\implies y = 2.5

Therefore , the point of intersection will be ,

\implies\underline{\underline{ Point = (-0.5,2.5 ) }}

You might be interested in
Determine the gradient of the straight line 2x-3y+9=0. Find the equation of the straight line through the origin which is perpen
frutty [35]

Answer: 3

x

−

2

y

−

15

=

0

Explanation:

We know that,

the slope of the line  

a

x

+

b

y

+

c

=

0

is  

m

=

−

a

b

∴

The slope of the line  

2

x

+

3

y

=

9

is  

m

1

=

−

2

3

∴

The slope of the line perpendicular to  

2

x

+

3

y

=

9

is  

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through  

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

)

⇒

2

y

+

6

=

3

x

−

9

⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through  

A

(

x

1

,

y

1

)

and

with slope

m

is

y

−

y

1

=

m

(

x

−

x

1

)3

x

−

2

y

−

15

=

0

Explanation:

We know that,

the slope of the line  

a

x

+

b

y

+

c

=

0

is  

m

=

−

a

b

∴

The slope of the line  

2

x

+

3

y

=

9

is  

m

1

=

−

2

3

∴

The slope of the line perpendicular to  

2

x

+

3

y

=

9

is  

m

2

=

−

1

m

1

=

−

1

−

2

3

=

3

2

.

Hence,the equn.of line passing through  

(

3

,

−

3

)

and

m

2

=

3

2

is

y

−

(

−

3

)

=

3

2

(

x

−

3

)

y

+

3

=

3

2

(

x

−

3

)

⇒

2

y

+

6

=

3

x

−

9

⇒

3

x

−

2

y

−

15

=

0

Note:

The equn.of line passing through  

A

(

x

1

,

y

1

)

and

with slope

m

is

y

−

y

1

=

m

(

x

−

Explanation:

the equation of a line in  

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange  

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m  

=

−

2

3

Given a line with slope then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

y

=

3

2

x

+

b

←

is the partial equation

to find b substitute  

(

3

,

−

3

)

into the partial equation

−

3

=

9

2

+

b

⇒

b

=

−

6

2

−

9

2

=

−

15

2

⇒

y

=

3

2

x

−

15

2

←

equation of perpendicular lineExplanation:

the equation of a line in  

slope-intercept form

is.

∙

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

rearrange  

2

x

+

3

y

=

9

into this form

⇒

3

y

=

−

2

x

+

9

⇒

y

=

−

2

3

x

+

3

←

in slope-intercept form

with slope m  

=

−

2

3

Given a line with slope then the slope of a line

perpendicular to it is

∙

x

m

perpendicular

=

−

1

m

⇒

m

perpendicular

=

−

1

−

2

3

=

3

2

⇒

y

=

3

2

x

+

b

←

is the partial equation

to find b substitute  

(

3

,

−

3

)

into the partial equation

−

3

=

9

2

+

b

⇒

b

=

−

6

2

−

9

2

=

−

15

2

⇒

y

=

3

2

x

−

15

2

←

equation of perpendicular line

7 0
3 years ago
Read 2 more answers
Find the measures of the labeled angles
Andrei [34K]

Answer:

135 degrees \

Step-by-step explanation:

5x= x+108

Subtract x from the right

4x= 108

divide by 4

x= 27

Substitute for x in the original equation

(x+108)

(27)+(108)

= 135 degrees

4 0
3 years ago
Piper is helping her dad lay out purple tiles to make completed they have done all of this they are 16 tiles and they filled it
9966 [12]

Answer:

9 tiles needed to fill

Step-by-step explanation:

16 - 7

6 0
3 years ago
A church group ordered a total of 22 drinks and burgers.each drink cost $2.50 and each burger cost $6.25 if the group spent a to
stepan [7]
14.8 or round up to 15 burgers
7 0
3 years ago
10. Which of the following situations represents a proportional relationship?....
tia_tia [17]

Answer:

G  A pool fills at a rate of 90 gallons per hour

Step-by-step explanation:

i dont know

7 0
2 years ago
Other questions:
  • PICTURE INCLUDED!
    11·2 answers
  • if there are 1,254 males born and 1,462 females what's the probability the next baby born will be a boy
    12·2 answers
  • Which postulate can be used to prove that the triangles are congruent?
    15·1 answer
  • Suppose Securitex is a small firm that has developed a new​ anti-theft device for automobiles. Securitex currently sells its dev
    7·1 answer
  • Round each number to the nearest tenth.
    9·2 answers
  • What is the greatest common factor of 2 16 and 12
    5·1 answer
  • 1.) <br> A.) tan 50°<br> B.) cot 50°<br> C.) sin 50°<br> D.) cos 50°<br> E.) cot 50°
    10·2 answers
  • Solve<br><br> 7x - 2 = 5x + 14
    9·1 answer
  • FAST PLEASE!! Emma weighs half as much as Sonya. Sonya weighs 120 pounds. How much
    13·1 answer
  • What must you do when you divide and multiply by a negative number?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!