Linear Equations in One Variable In this page we are going to discuss about linear equations in one variable concept. Online math equations of one variable with first order (the power is always one) is named as linear equation for one variable equations. The solution obtained is called the root for the given equation. The example for one variable equation is 4x + 2 =1. Online has emerged as one of the major source for students to develop their knowledge subject wise. In this article we shall discuss online help for one variable equations. Linear Equations in One Variable Examples Below you can see the examples on linear equations in one variable Solve the given one variable equations a - 7 = 2 Solution: Know More About Difference of Cubes
Add 7 on either side a-7+7=2+7 Now, simplify the expression on either side a=9 Thus, the value of a is 9. Problem 2: Solve the given one variable equations 5x = 20 Solution :- Divide by 5 on either side 5x5 = 205 Now, simplify the expression on either side x=4 Thus, the value of x is 4. Learn More About Dependent Variable Definition
Problem 3: aSolve the given one variable equations x3 = 5 Solve the given one variable equations 4x - 7 = - 10 Solution: Add 7 on either side 4x - 7 + 7 = -10 + 7 By simplify the expression on either side 4x = -3 Divide by 4 on either side 4x4 = −34 Reduce this expression on either side x = −34 Thus, the value of x is −34
Solve by Elimination Method In math, Elimination method is used in algebra course. In algebra, we use elimination method for solving systems of equations. There are two easy methods for solving systems of equations. They are substitution method and elimination method. Elimination method is sometimes more convenient than the substitution method. Elimination method is also known as Addition or subtraction method. In elimination method, one variable in the equation is eliminated by adding or subtracting the two equations. In this method, we eliminate one of the unknowns. Step 1 :- Multiply the given equations by suitable numbers so as to make the coefficients of one of the unknowns, numerically equal Step 2 :- Add the new equations, if the numerically equal coefficients are opposite in sign, otherwise, subtract them.
Step 3 :- The resulting equation is linear in one unknown. Solve it to obtain the value of one of the unknowns. Step 4 :- Substitute the value of this unknown in any of the given equations. Solve it to vet the value of the other unknown. Along with Elimination method for solving equations, students can also learn solving simultaneous equations by substitution method. What is Elimination MethodBack to Top Here is more examples on how to use elimination method for solving equations: Example 1:Solve Solution : The given equations are 5x + 6y = 13 …(i) 3x + 4y = 7 …(ii) Multiplying (i) by 3 and (ii) by 5, we get 15x + 18y = 39 …(iii) Read More About Boolean Algebra
15x + 20y = 35 …(iv) Subtracting (iv) from (iii), we get - 2y = 4 ⇒ y = - 2 Subtracting y = - 2 in (i), we get 5x + 6 × (- 2) = 13 ⇒ 5x - 12 = 13 ⇒ 5x = 251 ⇒ 25x = 5 ⇒ x = 525 = 15 Hence, x = and y = - 2 is the solution of the given equations Example 2: Solve 17x + 16y = 3, 12x - 13y = 5 Solution : The given equations are 17x + 16y = 3 …(i) 12x - 13y = 5 …(ii) Putting 1x = u and 1y = v, these equations become 17u + 16v = 3 ⇒ 6u + 7v = 126 …(iii) 12u - 13v = 5 ⇒ 3u - 2v = 30 …(iv) Multiplying (iv) by 2, we get 6u - 4v = 60 …(v)
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