Solve these equations.
a) $5 x-1=9$
b) $4 y+1=15$

Solve for x in the equation 5 x − 1 = 9 by adding 1 to both sides and then dividing by 5: x = 5 10 ​ = 2 .
Solve for y in the equation 4 y + 1 = 15 by subtracting 1 from both sides and then dividing by 4: y = 4 14 ​ = 3.5 .
The solution for x is 2.
The solution for y is 3.5, so the final answers are x = 2 ​ and y = 3.5 ​ .

Explanation

Problem Analysis We are given two linear equations and asked to solve for x and y . Let's solve each equation separately.

Isolating the x term a) To solve the equation 5 x − 1 = 9 for x , we first add 1 to both sides of the equation to isolate the term with x :
5 x − 1 + 1 = 9 + 1

Simplifying the equation Simplifying both sides, we get: 5 x = 10

Solving for x Now, we divide both sides by 5 to solve for x :
x = 5 10 ​

Finding the value of x Simplifying the fraction, we find the value of x :
x = 2

Isolating the y term b) To solve the equation 4 y + 1 = 15 for y , we first subtract 1 from both sides of the equation to isolate the term with y :
4 y + 1 − 1 = 15 − 1

Simplifying the equation Simplifying both sides, we get: 4 y = 14

Solving for y Now, we divide both sides by 4 to solve for y :
y = 4 14 ​

Finding the value of y Simplifying the fraction, we find the value of y :
y = 2 7 ​ = 3.5

Final Answer Therefore, the solutions are x = 2 and y = 3.5 .


Examples
Linear equations are used in many real-world scenarios, such as calculating the cost of items, determining the speed of a car, or predicting the growth of a population. For example, if you know the cost of a movie ticket and the amount of money you have, you can use a linear equation to determine how many tickets you can buy. Understanding how to solve linear equations is a fundamental skill in mathematics and has many practical applications.

Answered by GinnyAnswer | 2025-07-03

The solution for the equation 5 x − 1 = 9 is x = 2 , and for the equation 4 y + 1 = 15 , the solution is y = 3.5 .
;

Answered by Anonymous | 2025-07-04