# Solving Simultaneous Equations Without Using Calculator!

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## Solving the simultaneous equation!

Simultaneous Equations are equations involving two or more unknowns that are to have the same values in each equation. Simultaneous equations can be easily solved by using a calculator. Solving the simultaneous equation means finding the value of two unknowns that make them true.

The following steps will demonstrate how to solve simultaneous equations between linear equation and nonlinear equation. We are given two equations :

3x = y + 5 ---- 1 (linear equation)

y2 - 7 = 3x ---- 2 (nonlinear equation)

(I) Isolate one of the variables x or y of the linear equation.

y = 3x - 5.

(II) Substitute for the isolate variable x or y into the nonlinear equation.

(3x - 5)2 - 7 = 3x

(3x - 5)(3x - 5) - 7 = 3x

9x2 - 15x - 15x + 25 - 7 - 3x = 0

9x2 - 33x + 18 = 0

(III) Solve the quadratic equation by factorization or using the formula.

9x2 - 33x + 18 = 0

3x2 - 11x + 6 = 0

(3x - 2)(x - 3) = 0

x = 3 , x = 2/3

(IV) Solve the equation for the other variable x or y by substituting the value of variable y or x into the linear equation.

y = 3x - 5

x = 3 ; y = 3(3) - 5 = 4

x = 2/3 ; y = 3(2/3) - 5 = -3

Conclusion :

x = 3 ; y = 4

x = 2/3 ; y = -3