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Solve the simultaneous equations - Leaving Cert Mathematics - Question 1 - 2018
Question 1
Solve the simultaneous equations. egin{align*} 2x + 3y - z &= -4 \\ 3x + 2y + 2z &= 14 \\ x - 3z &= -13 ext{(i)} ext{(ii)} ext{(iii)} ext{Solve the inequality ... show full transcript
Worked Solution & Example Answer:Solve the simultaneous equations - Leaving Cert Mathematics - Question 1 - 2018
Step 1
Solve the simultaneous equations. (i)
Answer
To solve the system of equations, we can use substitution or elimination.
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From the first equation, isolate z:
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Substitute this expression for z into the other two equations:
- For the second equation: Simplifying this gives:
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Solving these two equations simultaneously will yield the values for x and y:
- Multiply the first equation by 5:
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Calculating this leads to x = 2 and when substituted back, y = -1 and then find z using initial substitution.
Step 2
Solve the inequality (b)
Answer
To solve the inequality ( \frac{2x - 3}{x + 2} \geq 3 ):
- Rewrite the inequality: This simplifies to: -x \geq 9 \ \\ x \leq -9$$
- Note that the inequality must also consider the values where the denominator is not zero: ( x + 2 \neq 0 \Rightarrow x \neq -2 ) .
Thus, the solution can be described as: ( x \leq -9 ) (and excluding -2) hence, the final solution is: