A=34.5. B=29.04. C= 204.7 D= 18.83

Find the point of intersection (if any) of the following pairs of lines: a) x – 2y +1=0 2x + 3y – 7 = 0 b) x-2y+11=0 -x+2y-13 =

pychu [463]

Answer:

a) (11/7, 9/7)

b) There's no point of intersection

Step-by-step explanation:

a) x - 2y + 1 = 0

2x + 3y - 7 = 0

To find the point of intersection, we need to solve the system of equations and the result will be the point of intersection (x,y)

$x-2y+1=0\\x= 2y-1$

Now we substitute x in the second equation:

$2x+3y-7=0\\2(2y-1)+3y-7=0\\4y-2+3y-7=0\\7y-9=0\\y=9/7$

Now we substitute y in our first equation.

$x-2y+1=0\\x-2(9/7)+1=0\\x-18/7+1=0\\x=18/7-1\\x=11/7$ .

The point of intersection is (11/7, 9/7)

b) x -2y +11 =0

-x + 2y - 13 =0

We are going to follow the same procedure:

$x-2y+11=0\\x=2y-11$

$-(2y-11)+2y-13=0\\-2y+11+2y-13=0\\0y=2\\0=2$

Since this system of equations doesn't have a solution, the system has no point of intersection.

5 0

2 years ago

Please Answer Quick 65 Points ! !

NeTakaya

The correct answers are:

The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.

The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.

Further explanation:

Given equations are:

2x-y = -5

x+3y = 22

We have to check whether the given statements are true or not. In order to find that we have to put the points in the equations

Putting the point in 2x-y = -5

$2x - y = -5\\2(7) -19 = -5\\14-19 = -5\\-5 = -5$

Putting the point in x+3y=22

$7 + 3 (19) = 22\\7 + 57 = 22\\64 \neq 22$

The point satisfies the first equation but doesn't satisfy the second. So,

1. The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.

This statement is true as the point satisfies the first equation

2. The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.

This Statement is false.

3. The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.

This statement is true.

4. The ordered pair (7, 19) is a solution to the system because it makes both equations true.

This statement is false as the ordered pair doesn't satisfy both equations.

Keywords: Solution of system of equations, linear equations

Learn more about solution of linear equations at:

#LearnwithBrainly

5 0

3 years ago

Solve the simultaneous equations -x + 5y = -7 x + y = – 5 x = 1 y= 0

vodomira [7]

y= -5-x

-x + 5(-5-x) = -7

-x -25-5x =-7

-x-5x = 25 -7

-6x= 18

x = -3

-3 +y = -5

y= -5 +3

=-2

-(-3) + 5(-2)

3 - 10 = -7

5 0

2 years ago

Read 2 more answers

Niko wants to buy a bicycle that costs $145. He has already saved $25. He says that he can determine the amount he still needs t

nevsk [136]

145 - 25 = b
b = 120

4 0

2 years ago

Read 2 more answers

Help pls :( Solve for x. -4 + 3x = 20

prohojiy [21]

$\huge\text{Hey there!}$

$\large\textsf{-4 + 3x = 20}\\\rightarrow\large\textsf{3x - 4 = 20}\\\\\large\text{ADD 4 to BOTH SIDES}\\\large\textsf{3x - 4 + 4 = 20 + 4}\\\large\text{CANCEL out: \textsf{-4 + 4} because that gives you \textsf 0}\\\large\text{KEEP: \textsf{20 + 4}} \text{ because it gives you the \textsf{x-value}}}\\\\\large\textsf{20 + 4 = \bf 24}\\\\\large\text{DIVIDE 3 to BOTH SIDES}\\\\\mathsf{\dfrac{3x}{3}= \dfrac{24}{3}}\\\large\text{CANCEL out: }\mathsf{\dfrac{3}{3}}\large\text{ because that gives you \textsf 1}$

$\large\text{KEEP: }\mathsf{\dfrac{24}{3}}\large\text{ because it helps gives you the result of the \textsf{x-value}}\\\\\mathsf{x = \dfrac{24}{3}}\\\\\large\textsf{x= 24}\div \large\textsf{3}}\\\large\textsf{x = \bf 8}\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 8}}}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~ $\frak{Amphitrite1040:)}$

3 0

3 years ago

Read 2 more answers