🧮 algebra

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x = 2y - 6 \\ y = 3x - 7 \end{cases}$$

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} x - 2y = 12 \\ y = 3x + 14 \end{cases}$$

1. Solve the system by substitution: Given: \( y = -x + 4 \) and \( y = 3x \).

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} y = 2x - 10 \\ 2y = x - 8 \end{cases}$$

1. **Énoncé du problème :** Simplifier l'expression $$\frac{2}{3} \times \left(2 + \frac{1}{4}\right)$$. 2. **Formule et règles importantes :** Pour multiplier une fraction par une

1. **Problem:** Solve the system using substitution: $$\begin{cases} y = -x + 4 \\ y = 3x \end{cases}$$

1. **Problem:** Solve the inequality $4x < -x$. 2. **Formula and rules:** To solve inequalities, we isolate $x$ on one side. When dividing or multiplying by a negative number, the

1. **State the problem:** Solve the quadratic equation $ax^2 + bx + c = 0$ for $x$. 2. **Formula used:** The quadratic formula is given by

1. Resuelve las raíces: **a)** $$\sqrt{48} - \sqrt{12} + \sqrt{3}$$

1. **نص المشكلة:** نريد إيجاد جذر للمعادلة $$x^4 + 2x = 4$$ في الفترة $$[1, 2]$$ باستخدام طريقة التنصيف (طريقة نصف القطر). 2. **صيغة المعادلة:** نعيد كتابة المعادلة على شكل دالة صف

1. **Énoncé du problème :** Déterminer les réels $a$, $b$, $c$ pour que l'hyperbole $R$ d'équation $$y = \frac{ax + b}{xc}$$ admette le point $\Omega\left(-1, \frac{1}{2}\right)$ c

1. **State the problem:** We have a cuboid with dimensions $x$ cm, $x$ cm, and $(15 - 4x)$ cm. 2. **Formula for volume:** The volume $V$ of a cuboid is given by the product of its

1. The problem asks us to simplify the fractions $\frac{8}{24}$ and $\frac{16}{56}$ to their lowest terms. 2. To simplify a fraction, we divide the numerator and denominator by the

1. **State the problem:** We are given two improper fractions: $\frac{28}{5}$ and $\frac{40}{5}$.

1. **State the problem:** We have 59 balls in total, divided into green, emerald, and maroon colors. 2. **Define variables:** Let $g$ be the number of green balls, $e$ the number o

1. **State the problem:** We have 30 phone cases in total, divided into three colors: emerald, turquoise, and orange. 2. **Define variables:** Let $E$ be the number of emerald case

1. **Problem:** Solve the equation $$x \cdot (4 + 5x) = (x + 2)^2 - 3(x + 1)(x - 1)$$. 2. **Formula and rules:** Expand both sides and simplify. Use distributive property and diffe

1. The problem appears to involve simplifying or evaluating the expression $4 \cdot 1 + \cos \theta \cdot 2 \cdot 2 \cos e x$. 2. First, rewrite the expression clearly: $$4 \times

1. **Problem statement:** A potter makes $x$ oval pots and $y$ bowl-shaped pots daily. 2. **Given:**

1. **State the problem:** Solve the linear equation $9 - 5x = 19$ for $x$. 2. **Formula and rules:** The equation is in the form $a - bx = c$. To solve for $x$, first isolate the t

1. **State the problem:** Solve the two-step equation $$\frac{1}{8}x + 11 = 12$$ for $x$ where the solution is a positive integer. 2. **Formula and rules:** The general form is $$\