Question

3. Is the equation true, false or open?

3y + 6 = 5y − 8




Now it’s your turn (Practice):

4. Is (5,15) a solution of the equation y = 3x?

5. Is (3,1) a solution of the equation y = −x + 3

Solve each equation. Check your answer.

7. −4 = z + 3

8. z − 10 = −1

9. 2.5 = 2x

10. −5 = z7

11. −15 = 52x

Answer 1

3. ∴ Equation is
`y-7=0.`

4. LHS = RHS Hence,
`(5, 15)` is a solution of a given equation.

5. LHS ≠ RHS Hence,
`(3, 1)` is not a solution of a given equation.

7.
`z=-7`

8.
`z=9`

9.
`x=1.25`

10.
`z=(-5)/(7) =-0.71428`

11.
`x=(-15)/(52) =-0.28846`

Explanation:

3. We have given the equation
`3y+6=5y-8`. Now, solving the given equation we get,

⇒
`5y-3y=6+8`

⇒
`2y=14`

⇒
`y=7`

∴ Equation is
`y-7=0.`

4. Given point is
`(5, 15)`, where
`x=5` and
`y=15`.

Now equation is
`y=3x`

⇒
`y-3x=0` (...
`i`)

now putting the value of
`x` and
`y` in equation (1), we get

⇒
`15-3*5=0`

⇒
`0=0` Here LHS = RHS Hence,
`(5, 15)` is a solution of a given equation.

5. Given point is
`(3, 1)`, where
`x=3` and
`y=1`.

Now equation is
`y=-x+3`

⇒
`y+x-3=0`
`(...ii)`

now putting the value of
`x` and
`y` in equation (11), we get

⇒
`1+3-3= 0`

⇒
`1\\eq 0` Here LHS ≠ RHS Hence,
`(3, 1)` is not a solution of a given equation.

7. Given equation is
`-4=z+3`

⇒
`z=-4-3`

⇒
`z=-7`

8. Given equation is
`z-10=-1`

⇒
`z=-1+10`

⇒
`z=9`

9. Given equation is
`2.5=2x`

⇒
`x=(2.5)/(2)`

⇒
`x=1.25`

10. Given equation is
`-5=z*7`

⇒
`z=(-5)/(7) =-0.71428`

11. Given equation is
`-15=52x`

⇒
`x=(-15)/(52) =-0.28846`