Solving Simultaneous Equations Using Substitution Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
3 of 53 of 5 Items

Question
Use the substitution method to solve the system 9x−3y=12
, y+6=2x
.(1 point)
(
)
Remaining Attempts : 3
Skip to navigation

Answer 1

To solve the system of equations using the substitution method, follow these steps:

We have:

1. \( 9x - 3y = 12 \) (Equation 1)
2. \( y + 6 = 2x \) (Equation 2)

Step 1: Solve one equation for one variable

Let's solve Equation 2 for \( y \): \[ y + 6 = 2x \] Subtract 6 from both sides: \[ y = 2x - 6 \]

Step 2: Substitute into the other equation

Now, substitute \( y = 2x - 6 \) into Equation 1: \[ 9x - 3(2x - 6) = 12 \]

Step 3: Simplify and solve for \( x \)

Distributing \(-3\): \[ 9x - 6x + 18 = 12 \] Combine like terms: \[ 3x + 18 = 12 \] Subtract 18 from both sides: \[ 3x = 12 - 18 \] \[ 3x = -6 \] Divide by 3: \[ x = -2 \]

Step 4: Substitute back to find \( y \)

Now substitute \( x = -2 \) back into the equation we derived for \( y \): \[ y = 2(-2) - 6 \] \[ y = -4 - 6 \] \[ y = -10 \]

Final Solution

The solution to the system of equations is: \[ (x, y) = (-2, -10) \]

You can check both equations to ensure that these values satisfy them.