Math Problem Statement

Solve the system of equations: y = 7x - 2 and y = 4x + 1

Solution

The image presents a system of two linear equations in two variables:

  1. y=7x2y = 7x - 2
  2. y=4x+1y = 4x + 1

This is likely asking to solve the system of equations using a method (based on the partial text: "menggunakan metode," which is Indonesian for "using the method"). The most common methods for solving such systems are substitution, elimination, or graphical methods.

Let's solve it using substitution:

  1. Since both equations are already solved for yy, we can set them equal to each other: 7x2=4x+17x - 2 = 4x + 1

  2. Solve for xx: 7x4x=1+27x - 4x = 1 + 2 3x=33x = 3 x=1x = 1

  3. Substitute x=1x = 1 into one of the original equations (e.g., y=7x2y = 7x - 2) to find yy: y=7(1)2=72=5y = 7(1) - 2 = 7 - 2 = 5

So, the solution to the system is: x=1,y=5x = 1, \quad y = 5

Would you like more details on this method or prefer to see another method like elimination?

Related questions:

  1. How does the elimination method work for solving systems of equations?
  2. Can all systems of linear equations be solved using substitution?
  3. What is the graphical interpretation of solving this system of equations?
  4. Are there cases where systems of equations have no solution or infinitely many solutions?
  5. How can systems of equations be used in real-life applications, such as business or physics?

Tip:

When both equations are already solved for one variable (like yy here), substitution is often the easiest method to use.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

Linear equation y = mx + c

Theorems

Equality of equations

Suitable Grade Level

Grades 8-10