Question

What is the answer to 9x-4y=7 x-4y=-17

Answer 1

The system of equations we have is:

`\begin{gathered} 9x-4y=7 \\ x-4y=-17 \end{gathered}`

To solve this system of equations and find the value of x and y, the steps are as follows:

Step 1. We will use the elimination method. In this method, we find the terms that have the same coefficient in both equations, and then subtract the equation to eliminate one variable.

In this case, we can see that in the first equation we have -4y, and also in the second equation we have -4y.

We subtract equation 2 from equation y to eliminate those terms:

We have to distribute the - sign to multiply all of the terms, and we get:

Now we can make the operations and the result is:

We have the equation:

`8x=24`

From here we can find x by dividing both sides of the equation by 8:

`\begin{gathered} (8x)/(8)=(24)/(8) \\ x=3 \end{gathered}`

Step 2. Now we need to find the value of y. To find it we use the value that we have just found for x, x=3, and substitute it on one of the initial equations.

We will use the first equation:

`9x-4y=7`

And substitute x=3:

`9(3)-4y=7`

Now we solve for y. First, multiply 9 times 3:

`27-4y=7`

Then, subtract 27 to both sides of the equation:

`\begin{gathered} -4y=7-27 \\ -4y=-20 \end{gathered}`

Finally, divide both sides of the equation by -4:

`(-4y)/(-4)=(-20)/(-4)`
`y=5`

Answer:

x=3 and y=5