Solve by elimination.
-4x + 9y = 9
x - 3y = -6
-4x + 9y = 9
Multiply second equation by 3.
3x - 9y = -18
Add the two equations.
-x = -9
x = 9
Insert x value in the first equation to find y.
9x+9y=9
-9x+y=-19
To solve this system of equations by elimination, we need to multiply one or both equations by a constant so that the coefficients of either x or y in one equation will be equal to the coefficients of x or y in the other equation.
Let's start by multiplying the second equation by 4 to eliminate x.
4(x - 3y) = 4(-6)
4x - 12y = -24
Now we have the following system of equations:
-4x + 9y = 9
4x - 12y = -24
Adding these two equations together will eliminate the x terms:
(-4x + 9y) + (4x - 12y) = (9) + (-24)
(-4x + 4x) + (9y - 12y) = -15
0x - 3y = -15
-3y = -15
Now we can solve for y by dividing both sides of the equation by -3:
-3y / -3 = -15 / -3
y = 5
Substituting the value of y back into one of the original equations, we can solve for x:
x - 3(5) = -6
x - 15 = -6
x = -6 + 15
x = 9
Therefore, the solution to the system of equations is x = 9 and y = 5.
To solve this system of equations by elimination, we need to eliminate one of the variables by adding the two equations together or subtracting one equation from the other.
In this case, let's eliminate the variable `x`. We can accomplish this by multiplying the second equation by 4 to make the coefficient of `x` the same magnitude as the first equation:
Original equations:
-4x + 9y = 9 ...(1)
x - 3y = -6 ...(2)
Multiply equation (2) by 4:
4(x - 3y) = 4(-6)
4x - 12y = -24 ...(3)
Now, we can add equations (1) and (3) together to eliminate `x`:
(-4x + 9y) + (4x - 12y) = 9 + (-24)
-4x + 4x + 9y - 12y = -15
-3y = -15
Divide both sides of the equation by -3 to solve for `y`:
y = -15 / -3
y = 5
Now that we have found the value of `y`, we can substitute it back into one of the original equations to solve for `x`. Let's use equation (1):
-4x + 9(5) = 9
-4x + 45 = 9
-4x = 9 - 45
-4x = -36
Divide both sides by -4 to solve for `x`:
x = -36 / -4
x = 9
Therefore, the solution to the system of equations is x = 9, y = 5.