Final answer:
The student asked how to solve a system of equations using elimination. By aligning the x-coefficients and subtracting the equations, the value of y was found to be approximately 1.57. Substituting this value into one of the original equations gave the value of x as approximately -1.29.
Step-by-step explanation:
The student asked for assistance with solving a system of equations using elimination. The two equations given are 4x + 9y = 9 and x - 3y = -6. To use elimination, we want to eliminate one variable so we can solve for the other. In this case, we can multiply the second equation by 4 to align the x-coefficients:
- Original second equation: x - 3y = -6
- Multiply entire equation by 4: 4(x - 3y) = 4(-6)
- Resulting equation: 4x - 12y = -24
Next, we subtract this new equation from the first equation:
- Original first equation: 4x + 9y = 9
- Resulting from subtraction: (4x + 9y) - (4x - 12y) = 9 - (-24)
- Simplified: 21y = 33
Now we can solve for y by dividing both sides by 21:
- 21y / 21 = 33 / 21
- y = 33 / 21
- y = 1.5714...
After finding the value of y, we substitute it back into one of the original equations to find x:
- Substitute y into the second equation: x - 3(1.5714...) = -6
- Solve for x: x = -6 + 3(1.5714...)
- x = -6 + 4.7142...
- x = -1.2857...
So the solution to the system of equations by elimination is approximately x = -1.29 and y = 1.57.