🧮 algebra

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-y + 2z = 12 \\ -x - 3y + z = 12 \\ -2x + y + 3z = -15 \end{cases}$$

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-x + 3y - z = -13 \\ 2x + y = -16 \\ x + 2y + 3z = -17 \end{cases}$$

1. **Problem 1:** Calculate the value of $x$ given the equation $x = 100 - 110$ and then evaluate $7x = x \times 10$. 2. **Step 1:** Calculate $x$:

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} x + 2y + 3z = 11 \\ -2x + y + 3z = 14 \\ 2x - 2y - z = 13 \end{cases}$$

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} 2x + 2y - z = 17 \\ 3x + 2y - 2z = 19 \\ 3x - y - 3z = -3 \end{cases}$$

1. সমস্যা: দেওয়া আছে $g(x) = x + \frac{1}{x} = 5$। প্রমাণ করতে হবে: $\left(x^2 - \frac{1}{x^2}\right)^2 = 525$। 2. সূত্র: আমরা জানি, $(a+b)^2 = a^2 + 2ab + b^2$ এবং $(a+b)(a-b) =

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases}-x + 2y + 2z = 18 \\ -x + y - 2z = -17 \\ -3y + 2z = 7 \end{cases}$$

1. **Problem Statement:** We have a list $T$ of 30 positive decimals, none of which is an integer. The sum of these decimals is $S$. We define an estimated sum $E$ by rounding each

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} x + 2y + 2z = 18 \\ x + y - 2z = 17 \\ 3y + 2z = 7 \end{cases}$$

1. **State the problem:** Solve the system of equations by elimination: $$\begin{cases} x - y - 2z = 2 \\ 2x + y - 2z = 17 \\ 3x - y - 3z = 3 \end{cases}$$

1. Problem 224: Find how many possible values of $x$ satisfy the equation $5 - \frac{6}{x} = x$. 2. Start by rewriting the equation:

1. **State the problem:** We need to find how many integers satisfy the inequality $$\frac{(x+2)(x+3)}{x-2} \geq 0$$ and are less than 5. 2. **Identify critical points:** The expre

1. **State the problem:** Simplify the expression $$-8a^{-4}b^{-3}$$ by writing it with positive exponents only and avoiding radicals. 2. **Recall the rule for negative exponents:*

1. **State the problem:** We need to find how many times the value of $2^{-17}$ is contained in the expression $$\frac{2^{-14} + 2^{-15} + 2^{-16} + 2^{-17}}{5}.$$ 2. **Recall the

1. **Problem Statement:** Find the power of a quotient, i.e., simplify the expression $$\left(\frac{a}{b}\right)^n$$ where $a$, $b$ are numbers and $n$ is an integer. 2. **Formula:

1. The problem is to simplify the expression $$\left(\frac{b}{a}\right)^m$$ where the power $m$ applies to both numerator and denominator. 2. The rule for powers of a fraction stat

1. Problem: Solve the exponential equation $2^{x-4} = 4a^{x-6}$ where $a > 0$ and $a \neq 1$.

1. **State the problem:** We need to solve the algebraic expression or equation provided by the user. Since no specific problem was given, please provide the problem statement for

1. **State the problem:** Simplify the expression $$\frac{X^3 - 3X^2 - 3}{X^2 - 1}$$. 2. **Recall the formula and rules:** The denominator is a difference of squares: $$X^2 - 1 = (

1. **State the problem:** Simplify the expression $$\frac{X^3 - 3X^2 - 3}{X^2 - 1}$$. 2. **Recall the formula and rules:** The denominator is a difference of squares: $$X^2 - 1 = (

1. **State the problem:** Simplify the expression $$\frac{X^3 - 3X^2 - 3}{X^2 - 1}$$. 2. **Recall the formula and rules:** The denominator is a difference of squares: $$X^2 - 1 = (