How would I work this out?
4x+3y=21
2x+y=8
x=___ y=___
4x+3y=21 (1)
2x+y=8 (2)
(1) - 2*(2):
y = 5
plugging this in one of the equations gives x = 3/2
To solve this system of equations, we will use the method of substitution.
Given equations:
1) 4x + 3y = 21
2) 2x + y = 8
First, let's solve one of the equations for one variable. Let's solve equation 2) for y:
2x + y = 8
Subtract 2x from both sides:
y = 8 - 2x
Next, substitute this expression for y into equation 1):
4x + 3(8 - 2x) = 21
Expand the expression:
4x + 24 - 6x = 21
Combine like terms:
-2x + 24 = 21
Subtract 24 from both sides:
-2x = 21 - 24
Simplify:
-2x = -3
Divide both sides by -2:
x = -3 / -2
Simplify:
x = 3/2
Now that we have found the value of x, we can substitute it back into one of the equations to solve for y. Let's use equation 2):
2(3/2) + y = 8
Simplify:
3 + y = 8
Subtract 3 from both sides:
y = 8 - 3
y = 5
Therefore, the solutions to the system of equations are: x = 3/2 and y = 5.