3a+b=52a+5=10use elimination to solve each systems of equations.
The way you typed it, there is no need to use elimination
from 52a+5 = 10
52a = 5
a = 5/52
sub into 3a + b = 10
3(5/52) + b = 10
times 52
15 + 52b = 520
52b = 505
b = 505/52
Whatever would make me think that you have a typo
To solve the system of equations using elimination, we need to eliminate one of the variables by adding or subtracting the equations. Let's solve the system step by step:
Equation 1: 3a + b = 5
Equation 2: 2a + 5 = 10 (Note: You may have made a typo in your question with the second equation. I assumed it to be "2a + 5 = 10")
Step 1: Multiply Equation 1 by 2 to make the coefficients of 'a' in both equations the same:
2 * (3a + b) = 2 * 5
6a + 2b = 10
Step 2: Now we have two equations with the same coefficient for 'a', so we can subtract Equation 2 from Equation 1 to eliminate 'a':
(6a + 2b) - (2a + 5) = 10 - 10
6a - 2a + 2b - 5 = 0
Simplifying this equation:
4a + 2b - 5 = 0
Now we have an equation with only one variable, 'b'. Let's solve for 'b':
Step 3: Isolate 'b' by moving the constant term to the other side of the equation:
4a + 2b = 5
Step 4: Subtract 4a from both sides:
2b = 5 - 4a
Step 5: Divide both sides by 2 to solve for 'b':
b = (5 - 4a) / 2
Now we have an expression for 'b' in terms of 'a'. Let's substitute this expression into either Equation 1 or Equation 2 to solve for 'a':
Using Equation 1:
3a + (5 - 4a) / 2 = 5
Simplifying this equation:
6a + 5 - 4a = 10
Step 6: Combine like terms:
2a + 5 = 10
Step 7: Move the constant term to the other side of the equation:
2a = 10 - 5
Step 8: Simplify:
2a = 5
Step 9: Divide by 2 to solve for 'a':
a = 5 / 2
So the solution to the system of equations is a = 5/2 and b = (5 - 4a) / 2.