Question

Select the statement that correctly describes the solution to this system of equations.4x+y=82x-3y=4A.There is no solution B.There are infinitely many solutions C.There is exactly one solution at (2,0)D.There is exactly one solution at (0,2)

Answer 1

In order to solve this system of linear equations, we just have to isolate one of the variables in one of the equations, then replace it into the other equation and solve for one of the variables, like this:

By taking the first equation and solveing for y, we get:

4x + y = 8

4x - 4x + y = 8 - 4x

0 + y = 8 - 4x

y = 8 - 4x

Now, let's replace 8 - 4x for y into the second equation:

2x - 3y = 4

2x - 3×(8 - 4x) = 4

2x - 3 ×8 - 3×4x = 4

2x - 24 + 12x = 4

Now combine like terms and solve for x:

2x + 12x - 24 = 4

14x - 24 = 4

14x - 24 + 24 = 4 + 24

14x = 28

14x/14 = 28/14

x = 2

Now that we know the value of x, we can replace it into y = 8 - 4x to get the value of y, like this:

y = 8 - 4×2

y = 8 - 8 = 0

Then, y equals 0.

Since these equations are independent of each other we can say that there is exactly one solution, and that is (2,0), the correct answer is option C