Use the substitution method to solve the system 9x−3y=12 , y+6=2x .(1 point)
Let's solve the second equation for y:
y+6=2x
Subtract 6 from both sides:
y = 2x - 6
Now, substitute this expression for y in the first equation:
9x - 3(2x - 6) = 12
Distribute the -3:
9x - 6x + 18 = 12
Combine like terms:
3x + 18 = 12
Subtract 18 from both sides:
3x = -6
Divide both sides by 3:
x = -2
Now, substitute this value for x in the second equation to solve for y:
y + 6 = 2(-2)
y + 6 = -4
Subtract 6 from both sides:
y = -10
Therefore, the solution to the system of equations is x = -2 and y = -10.
Use the substitution method to solve the system 2x+3y=4 , −4x−6y=−8 .(1 point)
Responses
no solution
(2−1)
(−1,2)
infinite solutions
Let's solve the second equation for x:
-4x - 6y = -8
Divide both sides by -2:
2x + 3y = 4
Now, we have:
2x + 3y = 4 ...(1)
2x + 3y = 4 ...(2)
Since the left sides of both equations are equal, we can equate the right sides:
4 = 4
This means that both equations represent the same line. Therefore, the system of equations has infinitely many solutions.