🧮 algebra

1. **State the problem:** Solve the system of equations using matrix elimination: $$\begin{cases} x_1 - 3x_2 = 5 \\ -x_1 + x_2 + 5x_3 = 2 \\ x_2 + x_3 = 0 \end{cases}$$

1. **State the problem:** Solve the system of linear equations: $$\begin{cases} x_1 - 3x_2 = 5 \\ -x_1 + x_2 + 5x_3 = 2 \\ x_2 + x_3 = 0 \end{cases}$$

1. **State the problem:** We need to sketch the curve of the function $$y = (x+3)(x+1)(x-2)$$. 2. **Formula and important rules:** This is a cubic polynomial function. To sketch it

1. **State the problem:** Solve the quadratic equation $$x^2 = 49$$ for $$x$$. 2. **Formula and rules:** To solve $$x^2 = a$$, we take the square root of both sides, remembering th

1. The problem is to understand and solve percentage questions. 2. Percentage means "per hundred" and is denoted by the symbol %.

1. Let's create a new algebra question involving quadratic equations. 2. Problem: Solve the quadratic equation $$2x^2 - 4x - 6 = 0$$.

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + y = 9 \\ 3x - y = 16 \end{cases}$$

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + y = 9 \\ 3x - y = 16 \end{cases}$$

1. **State the problem:** Solve the system of equations: $$3x + 4y = 2$$

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + 3y = -2 \\ 3x - 6y = 18 \end{cases}$$

1. **State the problem:** Solve the system of linear equations: $$x - y = 1$$

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} 2x + 3y = 8 \\ 5x + 6y = 17 \end{cases}$$

1. **State the problem:** A group of $x$ people agreed to contribute equally to buy books worth 1200.

1. **State the problem:** Solve the system of equations using elimination: $$\begin{cases} x - y = 4 \\ x + y = 2 \end{cases}$$

1. **Problem statement:** Two vehicles start from towns A and B, 360 km apart. The minibus leaves A at 8:15 am traveling at 90 km/h. The matatu leaves B 2 \frac{1}{3} hours later (

1. **Find the vertical asymptote of** $f(x) = \frac{x - 1}{2x + 4}$. - Vertical asymptotes occur where the denominator is zero and the numerator is not zero.

1. **State the problem:** Solve the equation $$\frac{2}{y} + \frac{8}{y} - \frac{1}{y} = 9$$ for $y$. 2. **Combine like terms:** Since all terms on the left have the same denominat

1. **State the problem:** We need to find the value of $k$ such that the compound inequality $$4 - \frac{x}{3} > 3x - k > -13$$ holds true. 2. **Rewrite the compound inequality as

1. **State the problem:** Solve the quadratic equation $$x^2 - 10x + 34 = 0$$ for $x$. 2. **Formula used:** The quadratic formula for solving $ax^2 + bx + c = 0$ is:

1. **State the problem:** Solve the quadratic equation $$60x^2 + 25x - 15 = 0$$ by factoring. 2. **Formula and rules:** To solve by factoring, we first factor the quadratic express

1. **Stating the problem:** We have six numbers with the following information: - Lowest number = 37