I need help with the linear equation:
10 - 0.5y = 1.5x and y = 0.5(6x + 40)
10 - 0.5y = 1.5x
-1.5x - 0.5y = -10
Multiply both sides by -2:
Eq1: 3x + y = 20
y = 0.5(6x+40)
y = 3x + 20
Eq2: -3x + y = 20
Add Eq1 and Eq2:
2y = 40
Y = 20
In Eq1. replace y with 20:
3x + 20 = 20
3x = 20-20 = 0
X = 0.
Solution Set: (x,Y) = (0,20).
To solve the given system of linear equations, we will first simplify the equations and then use substitution method or elimination method to find the values of x and y.
Given equations:
1) 10 - 0.5y = 1.5x
2) y = 0.5(6x + 40)
Let's begin by simplifying equation 2:
2) y = 0.5(6x + 40)
y = 3x + 20
Now we have two simplified equations:
1) 10 - 0.5y = 1.5x
2) y = 3x + 20
We can use the substitution method or elimination method to solve for x and y. Let's use substitution method:
Substitute equation 2) into equation 1):
10 - 0.5(3x + 20) = 1.5x
Now distribute -0.5 to the terms inside the parentheses:
10 - 1.5x - 10 = 1.5x
Combine like terms:
-1.5x = 1.5x
Add 1.5x to both sides:
0 = 3x
Divide both sides by 3:
0/3 = x
0 = x
Now substitute the value of x = 0 into equation 2) to find y:
y = 3(0) + 20
y = 0 + 20
y = 20
Hence, the solution to the given system of linear equations is x = 0 and y = 20.