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3 years ago

Solve the system of equations - x - y = 6 and 5x -7y=66 by combining the equations

Mathematics

1 answer:

DIA [1.3K]3 years ago

7 0

Answer: Let's solve for x.

−x−y=6

Step 1: Add y to both sides.

−x−y+y=6+y

−x=y+6

Step 2: Divide both sides by -1.

−x

−1

y+6

−1

x=−y−6

Answer:

x=−y−6

Let's solve for x.

5x−7y=66

Step 1: Add 7y to both sides.

5x−7y+7y=66+7y

5x=7y+66

Step 2: Divide both sides by 5.

7y+66

Answer:

Step-by-step explanation:

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Solve for the unknown variables

malfutka [58]

Answer:

This term is known as algebra.

Step-by-step explanation:

Algebra is all about solving for unknown values. Of course, in the primary phrase (question) it says, "Solve for the unknown variables," and the unknowns are unknown variables that have values that are unknown and must be found through algebraic processes.

<h2>What is an "algebra" in mathematics?</h2>

Variables like as x, y, and z are coupled with mathematical operations such as addition, subtraction, multiplication, and division to generate a meaningful mathematical statement. An algebraic expression is as basic as 2x + 4 = 8. Algebra is concerned with symbols, and these symbols are connected to one another through operators. It is more than just a mathematical concept; it is a skill that we all have without even realizing it. Understanding algebra as a concept is more important than solving equations and achieving the proper solution since it applies to all other disciplines of mathematics that you will learn or have previously learned.

<h3>What is Algebra?</h3>

Algebra is a field of mathematics that works with symbols and the mathematical operations that may be performed on them. These symbols, which have no set values, are referred to as variables. We frequently encounter values that change in our real-life issues. However, there is a continual requirement to represent these changing values. In algebra, these values are frequently represented by symbols such as x, y, z, p, or q, and these symbols are referred to as variables. Furthermore, these symbols are subjected to different mathematical operations such as addition, subtraction, multiplication, and division in order to determine the values. 3x + 4 = 28. Operators, variables, and constants are used in the algebraic formulas above. The integers 4, 28, and x are constants, and the arithmetic operation of addition is done. Algebra is a branch of mathematics concerned with symbols and the mathematical operations that may be applied to them. Variables are symbols that do not have predefined values. In our daily lives, we regularly face values that shift. However, there is a constant need to express these shifting values. These values are usually represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables. Furthermore, in order to ascertain the values, these symbols are subjected to various mathematical operations such as addition, subtraction, multiplication, and division. 3x + 4 = 28. The algebraic formulae above make use of operators, variables, and constants. The constants are the numbers 4, 28, and x, and the arithmetic operation of addition is done.

<h3>Branches of Algebra</h3>

The use of many algebraic expressions lessens the algebraic complexity. Based on the usage and complexity of the expressions, algebra may be separated into many branches, which are listed below:

Pre-algebra: The basic methods for expressing unknown values as variables help in the formulation of mathematical assertions. It facilitates in the transition of real-world problems into mathematical algebraic expressions. Pre-algebra entails creating a mathematical expression for the given problem statement.

Primary algebra: Elementary algebra is concerned with resolving algebraic expressions in order to arrive at a viable solution. Simple variables such as x and y are expressed as equations in elementary algebra. Based on the degree of the variable, the equations are classed as linear, quadratic, or polynomial. The following formulae are examples of linear equations: axe + b = c, axe + by + c = 0, axe + by + cz + d = 0. Primary algebra can branch out into quadratic equations and polynomials depending on the degree of the variables.

<h3>Algebraic Expressions</h3>

An algebraic expression is made up of integer constants, variables, and the fundamental arithmetic operations of addition (+), subtraction (-), multiplication (x), and division (/). An algebraic expression would be 5x + 6. In this situation, 5 and 6 are constants, but x is not. Furthermore, the variables can be simple variables that use alphabets like x, y, and z, or complicated variables that use numbers like

$x^2,x^3,x^n,xy,x^2y,$

and so forth. Algebraic expressions are sometimes known as polynomials. A polynomial is a mathematical equation that consists of variables (also known as indeterminates), coefficients, and non-negative integer variable exponents. As an example,

$5x^3+4x^2+7x+2=0$

Any equation is a mathematical statement including the symbol 'equal to' between two algebraic expressions with equal values. The following are the many types of equations where we employ the algebra idea, based on the degree of the variable: Linear equations, which are stated in exponents of one degree, are used to explain the relationship between variables such as x, y, and z. Quadratic Formulas: A quadratic equation is usually written in the form

$ax^2+bx+c=0,$