Solve the equation $5x - 10 = 3x + 2$.
John says that $x = 4$ is a solution of $x^2 - 2x - 8 = 0$. Show that John is correct.
Solve the simultaneous equations:
$$x... show full transcript
Worked Solution & Example Answer:Solve the equation $5x - 10 = 3x + 2$ - Junior Cycle Mathematics - Question 11 - 2015
Step 1
Solve the equation $5x - 10 = 3x + 2$.
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To solve the equation, we first rearrange it:
5x−10=3x+2
Subtracting 3x from both sides gives:
5x−3x−10=2
This simplifies to:
2x−10=2
Now, we add 10 to both sides:
2x=12
Finally, dividing both sides by 2 yields:
x = 6.$$
Step 2
Show that John is correct.
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To verify John's statement, we substitute x=4 into the equation:
42−2(4)−8=0.
Calculating the left-hand side:
16−8−8=0,
which simplifies to:
0=0.
Thus, John is correct since the equation holds true.
Step 3
Solve the simultaneous equations:
$$x + y = 11$$
$$x - y = -5.$$
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
We can start by expressing x from the second equation:
x=y−5.
Substituting this into the first equation results in:
(y−5)+y=11.
This simplifies to:
2y−5=11.
Adding 5 to both sides gives:
2y=16,
which leads to:
y=8.
Now substituting y back into x=y−5 gives:
x=8−5=3.
Thus, the solution of the simultaneous equations is x=3 and y=8.
Join the Junior Cycle students using SimpleStudy...
