Solve these equations.
a) [tex]$5 x-1=9$[/tex]
b) [tex]$4 y+1=15$[/tex]
Answer (2)
Add 1 to both sides of the equation 5 x − 1 = 9 to get 5 x = 10 .
Divide both sides by 5 to find x = 2 .
Subtract 1 from both sides of the equation 4 y + 1 = 15 to get 4 y = 14 .
Divide both sides by 4 to find y = 4 14 = 3.5 . The solutions are x = 2 , y = 3.5 .
Explanation
Problem Analysis We are given two linear equations and our goal is to find the values of the variables x and y that satisfy each equation.
Solving for x For equation a) 5 x − 1 = 9 , we want to isolate x . First, we add 1 to both sides of the equation: 5 x − 1 + 1 = 9 + 1
5 x = 10
The value of x Next, we divide both sides by 5: 5 5 x = 5 10
x = 2
Solving for y For equation b) 4 y + 1 = 15 , we want to isolate y . First, we subtract 1 from both sides of the equation: 4 y + 1 − 1 = 15 − 1
4 y = 14
The value of y Next, we divide both sides by 4: 4 4 y = 4 14
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 distances, and modeling relationships between variables. For example, if you know the cost of a taxi ride is $3 plus $0.50 per mile, you can use a linear equation to determine the total cost for any given distance. Similarly, in physics, linear equations can describe the motion of an object at a constant speed.
The solution to the equation 5 x − 1 = 9 is x = 2 , and the solution to the equation 4 y + 1 = 15 is y = 3.5 .
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