Solving a system of two linear equations

Published on October 26, 2024

Algebra

The solution to the system of equations x + 2y = 5 and 3x - y = 1 is x = 1 and y = 2, found using the elimination method.

Question

x + 2y = 5 3x - y = 1

Answer

We can solve this system of equations using elimination.

Step 1: Manipulate the equations to make the coefficients of one variable opposites.

Multiply the second equation by 2 to make the y coefficients opposites:

This simplifies to:

Step 2: Add the equations together to eliminate one variable.

Adding the two equations, we get:

This simplifies to:

Step 3: Solve for the remaining variable.

Divide both sides by 7:

Step 4: Substitute the value found in Step 3 back into either original equation to solve for the other variable.

Let’s use the first original equation:

Subtract 1 from both sides:

Divide both sides by 2:

Answer: The solution to the system of equations is

and

🚀 Try Free Math Help Now!🏠 Learn More Powerful Features

Related math solutions

Add Rational Expressions with the Same Denominator

Simplify x/(x − 7) + (4x − 1)/(x − 7) by adding the numerators and keeping the common denominator. The result is (5x − 1)/(x − 7), where x ≠ 7.

Algebraic Proof: Show That an Expression is Even

Prove algebraically that the expression n^2 - 2 - (n - 2)^2 is always an even number by expanding the brackets and factoring out a 2.

Solving a Cubic Equation by Factoring

This problem involves solving the cubic equation 2x^3 + 2x^2 - 24x = 0 by factoring out the greatest common factor and then factoring the resulting quadratic expression.

Solve (x^2 + x)/x = 8 and Find 2√x | Rational Equation Solution

Simplify the rational expression (x^2 + x)/x by factoring out x to get x + 1, then solve x + 1 = 8 to find x = 7, so 2√x = 2√7 ≈ 5.29.

Finding the Minimum Point by Completing the Square for y = x^2 - 10x + 9

Learn how to find the minimum coordinates of the quadratic curve y = x^2 - 10x + 9 by using the method of completing the square to rewrite the equation in vertex form.

🔎 Explore All Shared Math Solutions