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 - 21A) 7B) -2C) Infinitely many solutionsD) No solution3. 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-3B) 3x-5=3x+8-x C) 4y+5=4y-6 D) 7z+6=-7z-5
Accepted Solution
A:
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)
Given the equation: [tex]3(x-7)-x=2x-21[/tex] ⇒ expanding the bracket [tex]3x-21-x=2x-21[/tex] ⇒ collecting like terms [tex]2x-21=2x=21[/tex]
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 ----------------------------------------------------------------------------------------------------------------
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: [tex]8-(5x+2)=-5x-6[/tex] ⇒ Multiplying out the bracket [tex]8-5x-2=-5x-6[/tex] [tex]6-5x=-5x-6[/tex] [tex]-5x+6=-5x-6[/tex] ⇒ Not an identity