Question

fan+medal
A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5
Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.
Use any method to solve the equivalent system of equations (the new first equation with the original second equation).
Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

Answer 1

2x + 7y = 1 ----equation 1
-3x - 4y = 5 ----equation 2
multiply equation 1 with 3
(2x + 7y = 1) x3
6x + 21y = 3 ----equation 1'
multiply equation 2 with 2
(-3x - 4y = 5) x2
-6x -8y = 10 ----equation 2'
add equation 1' and 2'
6x + 21y = 3
+ -6x -8y = 10
13y = 13
y = 1
substitute y=1 to equation 1
2x + 7y =1
2x + 7(1) = 1
2x = 1- 7
2x = -6
x = -3
proving that those are the values of x and y, we'll go back to the original equations and plug in the values attained: x=-3, y=1
equation 1:
2x + 7y = 1
2(-3) + 7(1) = 1
-6 + 7 = 1
1=1 ok!
equation 2:
-3x - 4y = 5
-3(-3) - 4(1) = 5
9 - 4 = 5
5 = 5 ok!
therefore the values for x and y are -3 and 1 respectively

Answer 2

can I ask you one more question? Please?

Answer 3

@shinalcantara

Answer 4

ok

Answer 5

Several systems of equations are given below.
System 1
y = 6x – 1.5
y = –6x + 1.5
System 2
x + 3y = –6
2x + 6y = 3
System 3
2x –y = 5
6x – 3y = 15




Which system of equations is consistent-independent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is consistent-dependent? How many solutions will the system of equations have? Expain your answers.
Which system of equations is inconsistent-independent? How many solutions will the system of equations have? Expain your answers.

Answer 6

y = 6x - 1.5
y = -6x + 1.5
is that the given?
it's like ????????????????

Answer 7

Im a bit confused on that as well but thats what I was given.

Answer 8

y = 6x - 1.5 ----equation 1
y = -6x + 1.5 ----equation 2
add equations 1 and 2
2y = 0
y = 0
substitute y=0 to either equation 1 or 2. let's have equation 1
y = 6x - 1.5
0 = 6x - 1.5
6x = 1.5
x = 0.25

Answer 9

x + 3y = -6
2x + 6y = 3
is this the given?

Answer 10

Yes. All the systems I sent were given ^.^

Answer 11

x + 3y = -6 ----equation 1
2x + 6y = 3 ----equation 2
multiply equation 1 with 2
(x + 3y = -6) x2
2x + 6y = -12 -----equation 1'
subtract equation 1' from equation 2
2x + 6y = 3
- 2x + 6y = -12
0 + 0 = 15
notice that the answers aren't equal therefore this system of lines doesn't have solution

Answer 12

2x - y = 5 ------equation 1
6x - 3y = 15 -----equation 2
multiply equation 1 with 3
(2x - y = 5) x3
6x - 3y = 15 -----equation 1'
subtract equations 1' and 2
6x - 3y = 15
- 6x - 3y = 15
0 = 0
in this case, since the two equations are equal, then there are infinite solutions. It only means that whatever the values of x and y that will be plugged in to both equations will be true.