Question

Which properties justify the steps taken to solve the system? {3x-2y=104x-3y=14 drag and drop the answers into the boxes to match each step. put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse. {9x-6y=308x-6y=28 x = 2 3(2)-2y=10 6-2y=10 -2y=4 y=-2

Answer 1

To solve the system of equations {3x-2y=10, 4x-3y=14}, you can use the method of substitution. Substitute x = (2y + 10)/3 from the first equation into the second equation and solve for y. Substitute y = -2 back into the first equation to solve for x.

Step-by-step explanation:

To solve the system of equations {3x - 2y = 10, 4x - 3y = 14}, you can use the method of substitution. Here are the steps:

1. Start with the first equation: 3x - 2y = 10. Solve for x in terms of y: 3x = 2y + 10. Dividing both sides by 3, we get x = (2y + 10)/3.
2. Substitute x = (2y + 10)/3 into the second equation: 4((2y + 10)/3) - 3y = 14. Simplify and solve for y: (8y + 40)/3 - 3y = 14. Multiply both sides by 3 to get rid of the fraction: 8y + 40 - 9y = 42. Combine like terms: -y + 40 = 42. Subtract 40 from both sides: -y = 2. Multiply by -1 to solve for y: y = -2.
3. Substitute y = -2 back into the first equation to solve for x: 3x - 2(-2) = 10. Simplify: 3x + 4 = 10. Subtract 4 from both sides: 3x = 6. Divide by 3 to solve for x: x = 2.

As a result, the system of equations is solved and the solution is x = 2, y = -2.