what is the coordinate point for 2x+y=7, 3x-4y=5

Question

Select the coordinate point that is a solution to this system of equations. 

 

2x+y=7

3x-4y=5

 

 

Answer 1

2x + y = 7
3x - 4y = 5

 

We can solve this via substitution by moving the 2x to the other side in the first equation and put that into the second:

y = 7 - 2x

 

3x - 4(7 - 2x) = 5

3x -  28 + 8x = 5

11x - 28 = 5

11x = 33

x = 3

 

Now we can solve for y:

y = 7 - 2 * 3

y = 7 - 6

y = 1

 

Now to check:

3 * 3 - 4 * 1 = 5

9 - 4 = 5

5 = 5

 

So with x = 3 and y = 1, our coordinate will be (3, 1).