How to solve the system of equations below using elimination?
b = 2a+1
10a+b=5b+2
This is the original problem, and I came up with the above equations. The answer is 37, but I can't see how.
"You can represent the value of any two-digit number with the expression 10a + b, where a is the tens' place digit and b is the ones' place digit. For example, if a is 5 and b is 7, then the value of the number is 10(5) + 7, or 57. What two-digit number is described below?
-The ones' place digit is one more than twice the tens' place digit.
-The value of the number is two more than five times the ones' place digit."
To solve the system of equations using elimination, follow these steps:
Step 1: Rearrange the equations
Rearrange the first equation to isolate "a":
b = 2a + 1
Rearrange the second equation to have both variables on the same side:
10a + b = 5b + 2
-5b - b + 10a = 2
Step 2: Multiply equations
To eliminate one variable, we need to find a way to make the coefficients of either "a" or "b" in both equations equal. In this case, we can multiply the first equation by -5 to make the coefficients of "b" equal:
-5b = -10a - 5
Step 3: Add the equations
Now, add the two equations together:
(-5b) + (b) = (-10a - 5) + (10a)
This simplifies to:
-4b = -5
Step 4: Solve for "b"
Divide both sides by -4 to solve for "b":
b = -5 / -4
b = 5/4 or 1.25
Step 5: Substitute "b" value back into one of the original equations
Substitute b = 1.25 into the first equation:
1.25 = 2a + 1
Step 6: Solve for "a"
Subtract 1 from both sides:
0.25 = 2a
Divide by 2:
a = 0.25 / 2
a = 0.125 or 1/8
Therefore, the solution to the system of equations is a = 0.125 and b = 1.25.