Math Problem Statement

Determine the solution set of the system of linear equations by elimination: 2x + y = 10 and y = -x + 3.

Solution

The system of linear equations given in the image is:

  1. 2x+y=102x + y = 10
  2. y=x+3y = -x + 3

To solve this by elimination, we first substitute the second equation y=x+3y = -x + 3 into the first equation to eliminate yy.

Step 1: Substitute y=x+3y = -x + 3 into 2x+y=102x + y = 10:

2x+(x+3)=102x + (-x + 3) = 10

Step 2: Simplify the equation:

2xx+3=102x - x + 3 = 10 x+3=10x + 3 = 10

Step 3: Solve for xx:

x=103x = 10 - 3 x=7x = 7

Step 4: Substitute x=7x = 7 back into the second equation y=x+3y = -x + 3 to find yy:

y=(7)+3y = -(7) + 3 y=7+3y = -7 + 3 y=4y = -4

Thus, the solution to the system of equations is x=7x = 7 and y=4y = -4.

Solution set:

(x,y)=(7,4)(x, y) = (7, -4)

Would you like further details on elimination, or do you have any other questions?

Here are 5 questions to expand on this topic:

  1. What are other methods for solving a system of linear equations?
  2. How can substitution be used more generally to solve systems of equations?
  3. Can the graph of this system help visualize the solution?
  4. What does it mean geometrically when two lines intersect at one point?
  5. How would the solution change if the system had no solution or infinite solutions?

Tip: Always double-check your substitution to avoid simple mistakes in solving systems of equations!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Linear Equations
System of Equations
Elimination Method

Formulas

y = -x + 3
2x + y = 10

Theorems

Elimination Method
Substitution Method

Suitable Grade Level

Grades 8-10