Solve using the appropriate method. Substitution or Elimination.
y = 2x - 5, y = 1/2x + 1
This morning I posted a question that Bosnian was kind enough to help me with but it was the wrong question that I was looking at. Sorry but I could really use some help I have been working on these problems since 5am. Please HELP!!
substitution, substitute for y.
2x-5=1/2 x + 1
3/2 x=6
x=4
y= 2*4-5=3
No problem, I'm here to help you with your math problem. Let's solve the system of equations using both the substitution and elimination methods and compare the solutions.
Given equations:
y = 2x - 5 (equation 1)
y = 1/2x + 1 (equation 2)
Method 1: Substitution
Step 1: Solve equation 1 for y.
From equation 1, we can write: y = 2x - 5.
Step 2: Substitute the value of y in equation 2.
Replace the y in equation 2 with (2x - 5):
2x - 5 = 1/2x + 1.
Now we have a new equation only involving x.
Step 3: Solve for x in the newly formed equation.
To eliminate the fraction, we can multiply the whole equation by 2.
2(2x - 5) = 2(1/2x + 1)
4x - 10 = x + 2
Combine like terms:
4x - x = 2 + 10
3x = 12
Step 4: Solve for x.
Divide both sides of the equation by 3:
x = 12/3
x = 4
Now we have found the value of x.
Step 5: Substitute the value of x back into either equation to find y.
Using equation 1:
y = 2x - 5
y = 2(4) - 5
y = 8 - 5
y = 3
So the solution using the substitution method is (x, y) = (4, 3).
Method 2: Elimination
Step 1: Multiply equation 2 by 2 to eliminate the fractions.
2y = x + 2 (equation 3)
Step 2: Rearrange equation 3 to match the form of equation 1.
x = 2y - 2 (equation 4)
Step 3: Substitute the value of x from equation 4 into equation 1.
y = 2x - 5
y = 2(2y - 2) - 5
y = 4y - 4 - 5
y = 4y - 9
Combine like terms:
-3y = -9
Step 4: Solve for y.
Divide both sides of the equation by -3:
y = -9/-3
y = 3
Now we have found the value of y.
Step 5: Substitute the value of y back into either equation to find x.
Using equation 1:
y = 2x - 5
3 = 2x - 5
8 = 2x
Divide both sides of the equation by 2:
x = 8/2
x = 4
So, the solution using the elimination method is (x, y) = (4, 3).
Both methods yield the same solution, x = 4 and y = 3.