Question

1. Tony and his sister Maria have the same birthday but Tony is five years older than Maria. Let the variable x represent Tony's age and y represent Maria's age. Which graph represents the relationship between Tony's age and Maria's age?

2. Solve the equation:
3 ( x -7 ) - x = 2x - 21

A) 7
B) -2
C) Infinitely many solutions
D) No solution


3. Which equation is an identity?

a. 8-(5x+2)=-5x-6
b. 7z+10-z=8z-2(z-5)
c. 8m-4=5m+8-m
d. 6y+5=6y-5


4. Which equation has no solution?

A) 7v+2=8v-3
B) 3x-5=3x+8-x
C) 4y+5=4y-6
D) 7z+6=-7z-5

Answer 1

the answer is a

Explanation:

dont woory its right

Answer 2

Question 1:

Let Maria's age be 'x'
and Tony's age be 'x+5'

Turning this expression into a linear equation, we have
y = x + 5

Any linear equation will have the same form, y = mx + c, where m is the gradient and c is the y-intercept.

Matching this to y = x + 5, we have the gradient = 1 and the y-intercept = 5

The graph that shows a positive gradient and crosses the y-axis at 5 is the first graph (attached again below)

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Question 2:

Given the equation:

`3(x-7)-x=2x-21` ⇒ expanding the bracket

`3x-21-x=2x-21` ⇒ collecting like terms

`2x-21=2x=21`

Notice that the expression on the Left Hand Side is exactly the same with the expression on the Right Hand Side, this means the value of 'x' can be any value

Answer: Option C
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Question 3

An identity is when the Left Hand Side expression and the Right Hand Side is exactly the same. Let's check for each equation:

Option A:

`8-(5x+2)=-5x-6` ⇒ Multiplying out the bracket

`8-5x-2=-5x-6`

`6-5x=-5x-6`

`-5x+6=-5x-6` ⇒ Not an identity

Option B:

`7z+10-z=8z-2(z-5)`

`6z+10=8z-2z+10`

`6z+10=6z+10` ⇒ Identity

Option C:

`8m-4=5m+8-m`

`8m-4=4m+8` ⇒ Not identity

Option D:

`6y+5=6y-5` ⇒ Not identity

Answer: Option B
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Question 4

Option A:

`7v+2=8v-3`

`7v-8v=-3-2`

`-1v=-5`

`v=5` ⇒ the equation have a solution

Option B:

`3x-5=3x+8-x`

`3x-5=2x+8`

`3x-2x=8+5`

`x=13` ⇒ The equation has one solution

Option C:

`4y+5=4y-6`

`4y-4y=-6-5`

`0y=-11` ⇒ The equation has no solution

Option D:

`7z+6=-7z-5`

`7z+7z=-5-6`

`14z=-11`

`z=- (11)/(14)` ⇒ The equation has one solution

Answer: Option C