Question

Solve the system of equations using the substitution method with the given equations:

1. S2a - 36 = 7
2. 2a - b = 5

Find the values of 'a' and 'b' that satisfy both equations.

Answer 1

The system of equations is solved using the substitution method. The solution found is a = 21.5 and b = 38 by isolating one variable, substituting it into the other equation, and solving step by step.

Step-by-step explanation:

To solve the system of equations using the substitution method, we need to isolate one variable and substitute it into the other equation.

1. First, we take the second equation, 2a - b = 5, and solve for b:

• b = 2a - 5.

Now we substitute this expression for b into the first equation, S2a - 36 = 7:

• S2a - 36 = 7 → S*(2a) - 36 = 7
• We simplify the equation to find the value of a:
• Therefore, S = 7 + 36 = 43, which simplifies to 2a = 43.
• Now we can solve for a: a = 43 / 2 = 21.5.

With a solved, we substitute it back into the expression for b:

• b = 2*(21.5) - 5 = 43 - 5 = 38.

The solution for the system of equations is a = 21.5 and b = 38.