Question

Solve the equation
3x + 1/2y=8
1/2x + 2y=9

Answer 1

To solve this system of equations, we can use the method of substitution.

First, let's solve one of the equations for one of the variables in terms of the other variable.

From the first equation, we can isolate x:

3x + (1/2)y = 8
3x = 8 - (1/2)y
x = (8 - (1/2)y)/3

Now, we substitute this expression for x into the second equation:

(1/2)((8 - (1/2)y)/3) + 2y = 9

Let's simplify this equation step by step. First, distribute (1/2) to the expression inside the parentheses:

(1/2)(8 - (1/2)y)/3 + 2y = 9

Next, multiply (1/2)(8) and (1/2)(-1/2y) separately:

(4 - (1/4)y)/3 + 2y = 9

To eliminate the fractions, we can multiply the entire equation by the common denominator of 3:

3*((4 - (1/4)y)/3) + 3*2y = 9*3

This simplifies to:

4 - (1/4)y + 6y = 27

Now, let's solve for y:

4 + (23/4)y = 27

Subtract 4 from both sides:

(23/4)y = 23

Multiply both sides by (4/23):

y = 4

Now that we have the value of y, we can substitute it back into one of the original equations to solve for x.

Let's use the first equation:

3x + (1/2)(4) = 8

Multiply (1/2)(4):

3x + 2 = 8

Subtract 2 from both sides:

3x = 6

Divide both sides by 3:

x = 2

So the solution to the system of equations is x = 2 and y = 4.