Question

Solve the following system of equations for a and for b:

System of equations:
4a + 2b = 20
15a - 5b = 60
a. a = -2, b = 9
b. a = 3, b = 2
c. a = 2, b = 5
d. a = 1, b = 4

Answer 1

To solve the given system of equations, we can use substitution. By solving for one variable and substituting it into the second equation, we can find the values of a and b. The solutions are a = 4.4 and b = 1.2.

Step-by-step explanation:

To solve the system of equations:

4a + 2b = 20

15a - 5b = 60

We can use the method of elimination or substitution. Let's solve it using substitution:

From the first equation, we have:

4a + 2b = 20

Solving for a:

a = (20 - 2b) / 4

Substituting this value of a into the second equation:

15((20 - 2b) / 4) - 5b = 60

Simplifying this equation:

15(20 - 2b) - 20b = 240

Expanding and simplifying further:

300 - 30b - 20b = 240

Combining like terms:

-50b = -60

Dividing both sides by -50:

b = 1.2

Now, substitute the value of b back into the first equation to solve for a:

4a + 2(1.2) = 20

Simplifying:

4a + 2.4 = 20

Subtracting 2.4 from both sides:

4a = 17.6

Dividing both sides by 4:

a = 4.4

Therefore, the solutions to the system of equations are a = 4.4 and b = 1.2.