which method would be the simplest way to solve the system?
y= 1/2x
2x+3y=28
To solve the system of equations where:
y = (1/2)x
2x + 3y = 28
You can use substitution, which is the simplest method in this case because the first equation is already solved for y. Here are the steps:
1. Substitute the expression for y from the first equation into the second equation:
2x + 3(1/2)x = 28
2. Simplify and solve for x:
2x + (3/2)x = 28
(4/2)x + (3/2)x = 28
(4x + 3x) / 2 = 28
7x / 2 = 28
7x = 56
x = 56 / 7
x = 8
3. Now that you have the value for x, plug it back into the first equation to find y:
y = (1/2)x
y = (1/2)(8)
y = 4
Therefore, the solution to the system is x = 8 and y = 4.