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Solve the equation $5x - 10 = 3x + 2$ - Junior Cycle Mathematics - Question 11 - 2015

Question 11

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 $5x - 10 = 3x + 2$.

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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.

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Answer

To verify John's statement, we substitute $x = 4$ into the equation:

4^2 - 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: $$x + y = 11$$ $$x - y = -5.$$

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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 $y = 8$ .

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Solve the equation $5x - 10 = 3x + 2$ - Junior Cycle Mathematics - Question 11 - 2015

Worked Solution & Example Answer:Solve the equation $5x - 10 = 3x + 2$ - Junior Cycle Mathematics - Question 11 - 2015

Solve the equation $5x - 10 = 3x + 2$.

Show that John is correct.

Solve the simultaneous equations: $$x + y = 11$$ $$x - y = -5.$$

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