91Ó°ÊÓ

Solving equations involves finding the value of the variable that makes the equation true. In the given problem, we are dealing with a linear equation, which is an equation of the first degree. The goal is to find the value of the variable (in this case, \( y \)) when \( x \) is replaced with a specific number. To solve the equation, we perform a series of steps:

• Substitute the given value of \( x \) into the equation.
• Simplify the resulting expression to find \( y \).

After completing these steps, we find that when \( x = -1 \), \( y = 21 \). This process shows that the value of \( y \) is determined by substituting and simplifying the linear equation given the condition \( x = -1 \).

Algebraic expressions form the building blocks of equations. They are composed of variables, numbers, and arithmetic operations. In the exercise, the expression \(-10x + 11\) is presented.Variables like \( x \) and \( y \) represent unknown values that can be substituted with numbers. In our specific example, \( x \) was replaced by \(-1\) to allow calculations.The steps involve symbolically manipulating this expression according to the given condition. Simplifying algebraic expressions involves combining like terms and performing operations. For instance, \(-10(-1) + 11\) illustrates how substitution changes expression form before simplification, passing to the value \( y = 21 \) follows.

Arithmetic operations are at the heart of simplifying and solving equations. These operations include addition, subtraction, multiplication, and division. When solving the given equation, \(-10x + 11\), arithmetic operations are vital in simplifying the expression.First, multiplication is performed on \(-10(-1)\), resulting in \(10\), due to the rule of multiplication of negatives yielding a positive product. Next, addition is performed to combine \( 10 \) and \( 11 \), resulting in \( y = 21 \).Understanding arithmetic principles is crucial as they underpin every step in the process, ensuring that transformations are accurate and solutions are correct. Always follow operation rules as they help achieve precise results across all mathematical computations.