Use elimination to solve the system of equations. a+4b= –4𝑎+4𝑏= –4 a+10b= –16

Sure, let's solve the system of equations step by step using the elimination method.

The system of equations is:

1. a + 4b = -4
2. a + 10b = -16

Step 1: Align the equations

To use the elimination method, we need to align the equations so that like terms are vertically aligned. Our equations are already aligned.

Step 2: Subtract one equation from the other

Subtract the first equation from the second to eliminate 'a'.

(a + 10b) - (a + 4b) = -16 - (-4)

This simplifies to:

6b = -12

Step 3: Solve for 'b'

Divide both sides of the equation by 6 to solve for 'b':

b = -12 / 6 = -2

Step 4: Substitute 'b' into one of the original equations

Substitute 'b' = -2 into the first equation:

a + 4(-2) = -4

This simplifies to:

a - 8 = -4

Step 5: Solve for 'a'

Add 8 to both sides of the equation to solve for 'a':

a = -4 + 8 = 4

So, the solution to the system of equations is a = 4, b = -2.