(x+2)/(7)+(x)/(4)=2x-8 (2y-3x)/(3)+2y=3x+4

3 min read Jun 16, 2024

(x+2)/(7)+(x)/(4)=2x-8 (2y-3x)/(3)+2y=3x+4

Solving Systems of Linear Equations

This article will guide you through the process of solving a system of linear equations. We will be working with the following system:

Equation 1: (x + 2) / 7 + x / 4 = 2x - 8

Equation 2: (2y - 3x) / 3 + 2y = 3x + 4

Step 1: Simplify the Equations

For Equation 1:

Find a common denominator: Multiply the first term by 4/4 and the second term by 7/7. This gives us: (4(x + 2)) / 28 + (7x) / 28 = 2x - 8
Combine the terms on the left side: (4x + 8 + 7x) / 28 = 2x - 8 (11x + 8) / 28 = 2x - 8
Multiply both sides by 28: 11x + 8 = 56x - 224
Simplify: -45x = -232

For Equation 2:

Multiply both sides by 3: 2y - 3x + 6y = 9x + 12
Combine like terms: 8y - 3x = 9x + 12
Simplify: 8y = 12x + 12

Step 2: Solve for One Variable

Solving for x in Equation 1:

Divide both sides of Equation 1 by -45: x = -232 / -45 x = 5.16 (approximately)

Solving for y in Equation 2:

Divide both sides of Equation 2 by 8: y = (12x + 12) / 8 y = (3x + 3) / 2

Step 3: Substitute and Solve

Substitute the value of x (5.16) into the equation for y:

y = (3 * 5.16 + 3) / 2
y = (18.48) / 2
y = 9.24 (approximately)

Solution

Therefore, the solution to the system of linear equations is x = 5.16 and y = 9.24.

Important Note: This solution is an approximate solution, as we rounded the value of x during the process. You can use these approximate values to verify the solutions in the original equations.