Answer

Verified

341.4k+ views

**Hint:**

Here, we will use the method of elimination to find the solution of the given equations. We will first add the given equations and simplify it to find the value of variable \[x\]. Then we will substitute this value in one of the equations to get the value of \[y\].

**Complete step by step solution:**

The given linear equations are:

\[5x - y = 33\] ……………………………………………………\[\left( 1 \right)\]

\[7x + y = 51\] …………..………………………………………\[\left( 2 \right)\]

Now, we will add equations \[\left( 1 \right)\] and \[\left( 2 \right)\]. Therefore, we get

\[5x - y + 7x + y = 33 + 51\]

Adding and subtracting the like terms, we get

\[ \Rightarrow 12x = 84\]

Dividing both sides by 12, we get

\[ \Rightarrow x = \dfrac{{84}}{{12}}\]

\[ \Rightarrow x = 7\]

Now, by substituting \[x = 7\] in equation \[\left( 1 \right)\], we get

\[5\left( 7 \right) - y = 33\]

Multiplying the terms, we get

\[ \Rightarrow 35 - y = 33\]

Now, by rewriting the equation, we get

\[ \Rightarrow y = 35 - 33\]

Subtracting the terms, we get

\[ \Rightarrow y = 2\]

**Therefore, the solution for the \[5x - y = 33\] and \[7x + y = 51\] is \[x = 7\] and \[y = 2\]**

**Additional Information:**

The solution set for the linear equations of two variables and with only one equation can be obtained only by the method of substitution. But we know that the linear equation of two variables can be solved by elimination method, cross multiplication method and substitution method. We are using the method of elimination where one variable is eliminated either by adding or subtracting the equations.

**Note:**

We know that an equation is defined as a mathematical statement with an equality sign between the two algebraic expressions. Linear equations are a combination of constants and variables. Linear equation is defined as an equation with the highest degree as 1. We know that the solution set is a set of values which satisfies the relation between the two mathematical expressions.

Recently Updated Pages

The branch of science which deals with nature and natural class 10 physics CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Define absolute refractive index of a medium

Find out what do the algal bloom and redtides sign class 10 biology CBSE

Prove that the function fleft x right xn is continuous class 12 maths CBSE

Find the values of other five trigonometric functions class 10 maths CBSE

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.

Write the difference between soap and detergent class 10 chemistry CBSE

Give 10 examples of unisexual and bisexual flowers

Differentiate between calcination and roasting class 11 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE

a Why did Mendel choose pea plants for his experiments class 10 biology CBSE