Math Problem Statement

Solve using substitution.

y = x + 6 y = –x − 4

( , )

Solution

To solve this system of equations using substitution, we'll substitute the expression for yy from the first equation into the second equation.

Step 1: Write the equations

  1. y=x+6y = x + 6
  2. y=x4y = -x - 4

Step 2: Substitute the expression for yy from the first equation into the second equation

We know that y=x+6y = x + 6, so substitute this into the second equation:

x+6=x4x + 6 = -x - 4

Step 3: Solve for xx

Now solve for xx: x+6=x4x + 6 = -x - 4 Add xx to both sides: 2x+6=42x + 6 = -4 Subtract 6 from both sides: 2x=102x = -10 Divide by 2: x=5x = -5

Step 4: Substitute x=5x = -5 back into one of the original equations to find yy

Use the first equation y=x+6y = x + 6:

y=5+6=1y = -5 + 6 = 1

Final Answer

The solution to the system of equations is (x,y)=(5,1)(x, y) = (-5, 1).

Do you need further explanation or have any questions?

Related questions:

  1. How do you solve a system of linear equations using the elimination method?
  2. What are the different methods for solving a system of equations?
  3. How can you check if a solution is correct in a system of equations?
  4. What does it mean if a system of equations has no solution or infinitely many solutions?
  5. Can you solve a system of equations with more than two variables using substitution?

Tip:

When using substitution, always choose the equation where one variable is already isolated, as it simplifies the substitution process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Substitution Method

Formulas

y = x + 6
y = -x - 4

Theorems

Substitution method for solving systems of equations

Suitable Grade Level

Grades 7-9