Question

Question 1

Solve the system of equations and choose the correct answer from the list of options.
d + e = 15
−d + e = −5
Label the ordered pair as (d, e).
A (0, 0)
B (10, −5)
C (5, 10)
D (10, 5)
question2
A set of equations is given below:
Equation S: y = x + 9
Equation T: y = 2x + 1
Which of the following steps can be used to find the solution to the set of equations?
A x = 2x + 1
B x + 9 = 2x
C x + 1 = 2x + 9
D x + 9 = 2x + 1
Question 3
A set of equations is given below:
Equation C: y = 6x + 9
Equation D: y = 6x + 2
Which of the following options is true about the solution to the given set of equations?
A One solution
B No solution
C Two solutions
D Infinite solutions
question 4
Solve the system of equations and choose the correct answer from the list of options.
2x + y = −4
y = 3x + 2
A negative 6 over five comma negative 8 over 5
B negative 8 over 5 comma negative 6 over 5
C negative 5 over 6 comma negative 11 over 5
D negative 11 over 5 comma negative 6 over 5
question 5
A system of equations is given below:
y = –2x + 1
6x + 2y = 22
Which of the following steps could be used to solve by substitution?
A 6x + 2(−2x + 1) = 22
B −2x + 1 = 6x + 2y
C 6(−2x + 1) + 2y = 22
D 6(y = −2x + 1)

Answer 1

1. d
2. d
3. b
4. a
5. a
those are the answers to the questions

Answer 2

1.D

2.D

3.B

4.A

5.A

Explanation:

1.We are given that two equations

`d+e=15`

`-d+e=-5`

Adding two equations then we get

`2 e=10`

`e=(10)/(2)=5`

Substitute e=5 in equation one then we get

`5+e=15`

`d=15-5`

`d=10`

Hence, the ordered pair as (10, 5).

Therefore,Option D is true.

2.We are given that two equations

Equation S:
`y=x+9`

Equatin T:
`y=2x+1`

Using substitution method

Substitute the value of y from equation one in equation second then we get

`x+9=2x+1`

Therefore, option D is true.

3.We are given that two equations

Equation C :
`y=6x+9`

Equation D
`:y=6x+2`

The two equations can be written as

`6x-y+9=0`

`6x-y+2=0`

`a_1=6,b_1=-1,c_1=9`

`a_2=6,b_2=-1,c_2=2`

`(a_1)/(a_2)=(6)/(6)=1:1`

`(b_1)/(b_2)=(-1)/(-1)=1:1`

`(c_1)/(c_2)=(9)/(2)`

`(a_1)/(a_2)=(b_1)/(b_2)\\eq(c_1)/(c_2)`

Therefore, system of equations have no solution

Hence, option B is true.

4.We are given that two equations

`2x+y=-4`

`y=3x+2`

Using substitution method

Substitute value of y from equation second in equation one

Then we get

`2x+3x=2=-4`

`5 x=-4-2`

`5 x=-6`

`x=-(6)/(5)`

Substitute the value of x in equation second then we get

`y=3*( -(6)/(5))+2`

`y=(-18+10)/(5)`

`y=-(8)/(5)`

Hence, option A is true.

5.We are given that two equations

`y=-2x+1`

`6x+2y=22`

Using substitution method

Substitute value of y from equation one in second equation then we get

`6x+2(-2x+1)=22`

Hence, option A is true.