Question

Which equation shows how to use substitution to solve the system?

a - 2 + y = 32 – 4
b - y=3(6 + y) – 4
c - 6 = 3x - 4
d - 2 + (32 – 4) = 6

Answer 1

To solve the system using substitution: solve the second equation for y in terms of c, then substitute the value of y in the first equation to express a in terms of b and c.

Step-by-step explanation:

The given system of equations is:

a - 2 + y = 32 - 4b - y

y = 3(6 + y) - 4c - 6

Let's solve the second equation for y in terms of c:

y = 3(6 + y) - 4c - 6

y = 18 + 3y - 4c - 6

2y = 12 - 4c

y = 6 - 2c

Now substitute the value of y in the first equation:

a - 2 + (6 - 2c) = 32 - 4b - (6 - 2c)

a - 2 + 6 - 2c = 32 - 4b - 6 + 2c

a + 4 - 2c = 26 - 4b + 2c

Now, solve for a in terms of b and c:

a = 22 - 4b + 4c

So, the equation using substitution to solve the system is:

a = 22 - 4b + 4c