Question

Solve the system of linear equations by substitution

6x-9 = y

Y= -3x

Answer 1

To solve the system, substitute the second equation, y = -3x, into the first, 6x - 9 = y. Solving for x gives x = 1, and substituting this back into y = -3x gives y = -3. Thus, the solution is x = 1 and y = -3.

Step-by-step explanation:

To solve the system of linear equations by substitution, we start with the two equations provided: 6x - 9 = y and y = -3x. The goal is to substitute one equation into the other to find the values of x and y that satisfy both equations simultaneously.

First, let's substitute the second equation into the first one:

1. Replace y in the first equation with -3x (since y = -3x):
2. 6x - 9 = -3x
3. Add 3x to both sides of the equation:
4. 6x + 3x - 9 = 0
5. Combine like terms:
6. 9x - 9 = 0
7. Add 9 to both sides of the equation:
8. 9x = 9
9. Divide both sides by 9:
10. x = 1

Now that we have the value of x, we can substitute it back into either of the original equations to find y. Using the second equation:

1. Substitute x = 1 into y = -3x:
2. y = -3(1)
3. y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.