Solve this system using the substitution method.
a – 4b = 2
5a = 3b – 7
Solve using the substitution method and be sure to show all of your work.
Write a - 4b = 2 as a = 4b+2, thus:
5a = 3b - 7
5(4b + 2) = 3b - 7
20b + 10 = 3b - 7
17b + 10 = -7
17b = -17
b = -1
Therefore, a - 4b = 2 --> a - 4(-1) = 2 --> a + 4 = 2 --> a = -2
This means that a = -2 and b = -1
since a = 4b+2, use that to get
5(4b+2) = 3b-7
solve for b, and then you can get a
To solve the system of equations using the substitution method, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for 'a' in terms of 'b':
a - 4b = 2
Rearrange the equation to isolate 'a':
a = 2 + 4b
Now we can substitute this expression for 'a' into the second equation:
5a = 3b - 7
Replace 'a' with '2 + 4b':
5(2 + 4b) = 3b - 7
Simplify the equation:
10 + 20b = 3b - 7
Combine like terms:
20b - 3b = -7 - 10
17b = -17
Divide both sides of the equation by 17 to solve for 'b':
b = -17 / 17
Simplify:
b = -1
Now that we have found the value of 'b', we can substitute it back into the first equation to solve for 'a':
a - 4(-1) = 2
a + 4 = 2
Subtract 4 from both sides of the equation:
a = 2 - 4
a = -2
Therefore, the solution to the system of equations is 'a = -2' and 'b = -1'.