Solving a System of Linear Equations: x + y = 3 and 3x

Math Problem Statement

can you help solve this linear equation x + y = 3 3x - 2y = 4

Yes, let's solve the system of linear equations:

1. & \quad x + y = 3 \\ 2. & \quad 3x - 2y = 4 \end{align*}$$ ### Step 1: Solve the first equation for $$x$$ or $$y$$. From the first equation $$x + y = 3$$, solve for $$x$$: $$x = 3 - y$$ ### Step 2: Substitute $$x$$ into the second equation. Substitute $$x = 3 - y$$ into the second equation $$3x - 2y = 4$$: $$3(3 - y) - 2y = 4$$ Simplify the equation: $$9 - 3y - 2y = 4$$ $$9 - 5y = 4$$ ### Step 3: Solve for $$y$$. Subtract 9 from both sides: $$-5y = 4 - 9$$ $$-5y = -5$$ Now, divide by $$-5$$: $$y = 1$$ ### Step 4: Solve for $$x$$. Substitute $$y = 1$$ back into the equation $$x = 3 - y$$: $$x = 3 - 1$$ $$x = 2$$ ### Solution: The solution to the system is: $$x = 2, \quad y = 1$$ Would you like more details on the steps or have any questions? --- Here are 5 questions to expand your understanding: 1. How can you verify if the solution $$x = 2, y = 1$$ is correct? 2. Can you solve the system using substitution for $$y$$ instead of $$x$$? 3. How would you graph these two equations and find their point of intersection? 4. What is the general method to solve a system using the elimination technique? 5. How would the solution change if the second equation were $$3x + 2y = 4$$? **Tip:** Always check your solutions by substituting the values back into both original equations.

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Algebra
Linear Equations
Systems of Equations

Substitution Method
Simplification of Equations

Substitution Method
Linear Equation Theorem

Grades 8-10

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