Solving System of Linear Equations: y=3x+2 and y=x-4

Math Problem Statement

What is the value of x in the solution to the system of linear equations? {y=3x+2 y=x-4 -7 -3 1 5

Let's solve the given system of linear equations:

y &= 3x + 2 \quad \text{(Equation 1)} \\ y &= x - 4 \quad \text{(Equation 2)} \end{aligned}$$ ### Step 1: Set the two equations equal to each other Since both equations equal $$y$$, we can set them equal to each other: $$3x + 2 = x - 4$$ ### Step 2: Solve for $$x$$ Now, solve the equation: $$3x + 2 = x - 4$$ Subtract $$x$$ from both sides: $$3x - x + 2 = -4$$ This simplifies to: $$2x + 2 = -4$$ Now, subtract 2 from both sides: $$2x = -6$$ Finally, divide both sides by 2: $$x = -3$$ ### Step 3: Find $$y$$ Now that we know $$x = -3$$, we can substitute this value into either of the original equations to find $$y$$. Let’s use Equation 2: $$y = x - 4$$ Substitute $$x = -3$$: $$y = -3 - 4 = -7$$ ### Final Answer: The solution to the system of equations is: $$x = -3 \quad \text{and} \quad y = -7$$ Would you like any more details on solving systems of equations? Or do you have other questions? ### Related Questions: 1. How can you solve a system of linear equations using substitution? 2. What is the graphical method of solving a system of equations? 3. How do you handle a system of equations with no solution or infinite solutions? 4. What is the method of solving systems of equations by elimination? 5. How do you solve a system of three equations with three unknowns? **Tip**: Always check the solution by substituting the values of $$x$$ and $$y$$ into both original equations to ensure they satisfy both.

Drop file here or Click Here to upload

Algebra
Systems of Linear Equations
Substitution Method

y = 3x + 2
y = x - 4

Substitution method for solving systems of equations

Grades 7-9

Solving Systems of Equations Using Substitution: y = 2x + 3, y = x + 2

Solving a System of Linear Equations: x + y = 3 and 3x - 2y = 4

Solving a System of Linear Equations Using Substitution: y = -3x - 2 and x - 3y = -4

Solving Systems of Equations by Substitution: Example with 3x-2y=4 and x=5y-3

Solving the System of Equations: x + y = 4 and y = 3x using Substitution