Solve the system of equations.
6x−3y=−6
9x−3y=−18 (1 point)
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To solve the system of equations, we can use the method of elimination. We can rearrange the second equation to have the same coefficient for y as the first equation:
9x - 3y = -18
-3y = -9x - 18
Dividing both sides by -3, we get:
y = 3x + 6
Now we can substitute this value of y into the first equation:
6x - 3(3x + 6) = -6
6x - 9x - 18 = -6
-3x - 18 = -6
-3x = 12
x = -4
Substituting this value of x back into the equation for y:
y = 3(-4) + 6
y = -12 + 6
y = -6
Therefore, the solution to the system of equations is (x, y) = (-4, -6).
To solve the system of equations, we can use the method of elimination or substitution. Let's use the method of elimination:
Step 1: Multiply the first equation by 3 to make the coefficients of "y" the same in both equations:
3 * (6x - 3y) = 3 * (-6)
18x - 9y = -18
Step 2: Rewrite the second equation:
9x - 3y = -18
Now we have the following system of equations:
18x - 9y = -18 ...(Equation 1)
9x - 3y = -18 ...(Equation 2)
Step 3: Multiply equation 2 by -2 to make the coefficients of "x" the same in both equations:
-2 * (9x - 3y) = -2 * (-18)
-18x + 6y = 36
Now we have the following system of equations:
18x - 9y = -18 ...(Equation 1)
-18x + 6y = 36 ...(Equation 3)
Step 4: Add equation 1 and equation 3 to eliminate "x" variable:
(18x - 9y) + (-18x + 6y) = (-18) + 36
-3y + 6y = 18
3y = 18
y = 18/3
y = 6
Step 5: Substitute the value of y = 6 into either equation 1 or equation 2 to find the value of x. Let's use equation 1:
18x - 9(6) = -18
18x - 54 = -18
18x = -18 + 54
18x = 36
x = 36/18
x = 2
Therefore, the solution to the system of equations is:
x = 2,
y = 6