Question

Solve the system of linear equation by substitution.
b = -3a - 7
b = a + 9
Solution: (☐, ☐)

Answer 1

-3a+b=-7

b=a+9

By substituting value of b=a+9 in - 3a+b=-7

-3a+a+9=-7

-2a=-16

a=8

b=17

Answer 2

Let's start by solving for a.

Take the first equation, b = -3a - 7, and substitute in the second equation, b = a + 9, for b.

We now have:

a+ 9 = -3a - 7

Add 3a to both sides.

4a + 9 = -7

Subtract 9 from both sides.

4a = -16

Divide each side by 4.

a = -4

Let's use the second equation, b = a + 9, to solve for a.

Put in the value we just solved for.

We now have:

b = -4 + 9

Simplify.

b = 5

Let's check our answer, starting with the first equation, b = -3a - 7.

Put in the values for a and b.

5 = -3(-4) - 7

5 = 12 - 7

5 = 5

Do the same with the second equation, b = a + 9.

5 = -4 + 9

5 = 5

The solution to the system of equations is (5, -4).