Question

State the number of solutions the given system of equations has: x=2y-4 3x-2y=4

Answer 1

The given system of equations has a unique solution: x = 4 and y = 4.

Step-by-step explanation:

The given system of equations is:

x = 2y - 4

3x - 2y = 4

We can solve this system of equations using the method of substitution or elimination. Let's use the method of substitution:

Step 1: Solve the first equation for x in terms of y:

x = 2y - 4

Step 2: Substitute this expression for x in the second equation:

3(2y - 4) - 2y = 4

Simplify and solve for y:

6y - 12 - 2y = 4

4y = 16

y = 4

Step 3: Substitute the value of y back into the first equation to find x:

x = 2(4) - 4

x = 8 - 4

x = 4

Therefore, the system of equations has a unique solution, x = 4 and y = 4.