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System Linear Equations3.1. Substitution MethodExample: Solve the linear equation in three methods                        4x + y = 6 -------------①                       5x + 3y = 4 ------------②

Question

System Linear Equations3.1. Substitution MethodExample: Solve the linear equation in three methods                        4x + y = 6 -------------①                       5x + 3y = 4 ------------②

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Solution

To solve the given system of linear equations using the substitution method, follow these steps:

Step 1: Choose one of the equations and solve it for one variable in terms of the other variable. Let's choose equation (①) and solve it for y: 4x + y = 6 y = 6 - 4x

Step 2: Substitute the expression for y obtained in step 1 into the other equation. Let's substitute y = 6 - 4x into equation (②): 5x + 3(6 - 4x) = 4

Step 3: Simplify and solve the resulting equation for x: 5x + 18 - 12x = 4 -7x + 18 = 4 -7x = 4 - 18 -7x = -14 x = -14 / -7 x = 2

Step 4: Substitute the value of x obtained in step 3 back into either of the original equations to solve for y. Let's substitute x = 2 into equation (①): 4(2) + y = 6 8 + y = 6 y = 6 - 8 y = -2

Therefore, the solution to the given system of linear equations is x = 2 and y = -2.

This problem has been solved

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