Math Problem Statement

Solve: y = 6 − 3x 2x + y = 5

Solution

To solve the system of equations:

  1. y=63xy = 6 - 3x
  2. 2x+y=52x + y = 5

We can use the substitution method.

First, substitute the expression for yy from the first equation into the second equation:

2x+(63x)=52x + (6 - 3x) = 5

Now, simplify and solve for xx:

2x+63x=52x + 6 - 3x = 5

x+6=5-x + 6 = 5

x=56-x = 5 - 6

x=1-x = -1

x=1x = 1

Now, substitute x=1x = 1 back into the first equation to solve for yy:

y=63(1)y = 6 - 3(1)

y=63y = 6 - 3

y=3y = 3

So, the solution to the system of equations is x=1x = 1 and y=3y = 3.

Would you like more details or have any questions about this solution? Here are some more questions you can ask:

  1. Can you explain how to solve a different system of equations?
  2. How do you solve a quadratic equation?
  3. What is the method for solving inequalities?
  4. Can you explain how to graph linear equations?
  5. How do you solve a system of equations using the elimination method?

Tip: Always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Substitution Method

Formulas

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Theorems

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Suitable Grade Level

High School