Question

Here is a system of linear equations:

2x + 1 / 2y=7
6x - 1/2y=5
Solve the system without graphing. Show your reasoning.
Use the equation editor button ( x ) as needed.

Answer 1

To solve the system of linear equations without graphing, use the method of substitution. The solution to the given system of equations 2x + 1/2y = 7 and 6x - 1/2y = 5 is x = 3/2 and y = 8.

Step-by-step explanation:

To solve the system of linear equations without graphing, we can use the method of substitution. Let's solve the first equation for x:

2x + 1/2y = 7

Multiplying both sides of the equation by 2, we get:

4x + y = 14

Now, solve the second equation for y:

6x - 1/2y = 5

Multiplying both sides of the equation by 2, we get:

12x - y = 10

Now, we have the system of equations:

4x + y = 14

12x - y = 10

We can add the two equations to eliminate y:

(4x + y) + (12x - y) = 14 + 10

16x = 24

Dividing both sides of the equation by 16, we get:

x = 3/2

Substituting this value of x into one of the original equations, we can solve for y:

2(3/2) + 1/2y = 7

3 + 1/2y = 7

1/2y = 4

y = 8

Therefore, the solution to the system of equations is x = 3/2 and y = 8.