Question

Which ordered pair is a solution of the linear system shown? Please include & show all your work to solve this problem.

y = 1/2x + 1

y = 3/2x + 4

A. (-3, -1/2)
B. (0,1)
C. (3/2, 7/4)
D. (3, 5/2)

Answer 1

Answer: A

If you plug in -3 into X on both equations you'd get -1/2, thus showing that (-3, -1/2) is a solution to both

Answer 2

To find the solution of a linear system, we need to find the values of x and y that satisfy both equations. One method to solve a system of linear equations is substitution. We can use the first equation to find the value of y in terms of x, and substitute it into the second equation.

y = 1/2x + 1

y = 3/2x + 4

We substitute the first equation into the second equation:

3/2x + 4 = 1/2x + 1

Now we simplify:

2x = 3

x = 3/2

Finally, we substitute x = 3/2 into either equation to find y:

y = 1/2 * 3/2 + 1 = 2

So, the solution of the system is (3/2, 2). Out of the given options, only (3/2, 7/4) has the same values of x and y.

Therefore, the answer is (C) (3/2, 7/4).