Select the set of equation that represents the following situation: The sum of two numbers is 52, and their differewnce is two less than the smaller number. What are the two numbers?
2x= 52;52=x+2
x+y=52;y-x=x-2
x+y=52;x-y=2-x
2y=52;52=x-2
x+y=52;y-x=x-2
determine whether the point (1,4) is a solution of the system.
6x+9y=42 5x=0y=5
by substituting the point into each equation.
To represent the given situation mathematically, let's assume that the two numbers are x and y.
1. "The sum of two numbers is 52" can be represented by the equation:
x + y = 52
2. "Their difference is two less than the smaller number" can be represented by the equation:
y - x = x - 2
Now, we have a system of two equations:
x + y = 52
y - x = x - 2
To solve this system, we can use the elimination method or substitution method. I will demonstrate how to solve it using the elimination method:
Step 1: Multiply the second equation by -1 to eliminate the x term:
-1 * (y - x) = -1 * (x - 2)
-y + x = -x + 2
Step 2: Add the modified second equation to the first equation:
(x + y) + (-y + x) = 52 + (-x + 2)
Simplifying:
x + y - y + x = 52 - x + 2
2x = 54 - x
Step 3: Move the x term to one side:
2x + x = 54
3x = 54
Step 4: Solve for x by dividing both sides by 3:
x = 18
Now, substitute the value of x into one of the original equations to find y:
x + y = 52
18 + y = 52
Solving for y:
y = 52 - 18
y = 34
Therefore, the two numbers are x = 18 and y = 34.