Question

On your own paper, solve the system of equations using elimination and identify the

solution. Always list your answers alphabetically in the ordered pairs.
2a + 6z = 4
3a – 7z = 6
a) (a,z)=(1,−1)

b) (a,z)=(−2,1)

c) (a,z)=(3,2)

d) (a,z)=(0,−2)

Answer 1

To solve the system of equations, we use the elimination method by multiplying one or both equations to eliminate a variable and find the values of 'a' and 'z'. The solution to the system of equations is (a,z) = (2,0).

Step-by-step explanation:

To solve the system of equations using elimination, we need to eliminate one variable by multiplying one or both of the equations by appropriate constants such that when added together, one of the variables cancel out. Let's solve the system:

Equation 1: 2a + 6z = 4

Equation 2: 3a - 7z = 6

Multiplying Equation 1 by 3 and Equation 2 by 2 to eliminate variable 'a', we get:

6a + 18z = 12

6a - 14z = 12

Now subtracting these two equations, we get:

32z = 0

Dividing by 32 on both sides, we find that z = 0.

Substituting the value of z into either Equation 1 or Equation 2, we find:

2a = 4

Simplifying, we find that a = 2.

Therefore, the solution to the system of equations is (a,z) = (2,0).