Solving a System of Linear Equations Using Elimination Method

Math Problem Statement

Solve the system of equations: 2x1 + x2 = 8 and 4x1 - 3x2 = 6

The image contains the following system of linear equations:

2x_1 + x_2 = 8 \\ 4x_1 - 3x_2 = 6 \end{cases}$$ Let's solve this system using the substitution or elimination method. I'll use the elimination method here. ### Step 1: Make the coefficients of $$x_1$$ equal We can multiply the first equation by 2 to match the coefficients of $$x_1$$: $$\begin{cases} 4x_1 + 2x_2 = 16 \\ 4x_1 - 3x_2 = 6 \end{cases}$$ ### Step 2: Subtract the equations Subtract the second equation from the first to eliminate $$x_1$$: $$(4x_1 + 2x_2) - (4x_1 - 3x_2) = 16 - 6$$ $$5x_2 = 10$$ $$x_2 = 2$$ ### Step 3: Substitute $$x_2$$ back into one of the original equations Substitute $$x_2 = 2$$ into the first equation: $$2x_1 + 2 = 8$$ $$2x_1 = 6$$ $$x_1 = 3$$ ### Solution The solution to the system is: $$x_1 = 3, \quad x_2 = 2$$ Would you like more details or have any questions? Here are 5 related questions for further practice: 1. Solve the system: $$3x_1 + 4x_2 = 7$$ and $$6x_1 - 8x_2 = -10$$. 2. What is the graphical interpretation of solving a system of two linear equations? 3. How can you check if a system of linear equations has no solution or infinitely many solutions? 4. Solve $$5x_1 - 2x_2 = 12$$ and $$7x_1 + 3x_2 = -1$$. 5. Can a system of two linear equations be solved using matrices? If yes, how? **Tip:** When using the elimination method, ensure that the coefficients of one variable are made equal in both equations to easily eliminate that variable.

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Algebra
Systems of Linear Equations

Elimination method for solving systems of linear equations

None

Grades 8-10

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