Question

solve the system by substitution.
9x + y = 21
-x - 3 = y

Explanation:

Step1: Identify substitution equation

We have \( y = -x - 3 \) from the second equation.

Step2: Substitute \( y \) into first equation

Substitute \( y=-x - 3 \) into \( 9x + y=21 \):
\( 9x+(-x - 3)=21 \)
Simplify: \( 9x - x-3 = 21 \)
\( 8x-3 = 21 \)

Step3: Solve for \( x \)

Add 3 to both sides: \( 8x=21 + 3=24 \)
Divide by 8: \( x=\frac{24}{8}=3 \)

Step4: Solve for \( y \)

Substitute \( x = 3 \) into \( y=-x - 3 \):
\( y=-3 - 3=-6 \)

Answer:

The solution to the system is \( x = 3 \) and \( y=-6 \), or the ordered pair \( (3, -6) \).