solve by substitution.
0.5x+0.25y=36
y+18=16x
y + 18 = 16 x
y = 16 x - 18
______________
0.5 x + 0.25 y = 36
x / 2 + y / 4 = 36 Multiply both sides with 4
4 x / 2 + 4 y / 4 = 36 4
2 x + y = 144
2 x + 16 x - 18 = 144
18 x = 144 + 18
18 x = 162 Divide both sides with 18
x = 162 / 18
x = 9
y = 16 x -18
y = 16 9 - 18
y = 144 - 18
y = 126
Solutions :
x = 9 , y = 126
Proof :
0.5 x + 0.25 y = 36
x / 2 + y / 4 =
9 / 2 + 126 / 4 =
18 / 4 + 126 / 4 =
144 / 4 = 36
y + 18 = 16x
126 + 18 = 16 9
144 = 144
To solve the system of equations using the method of substitution, we need to solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the second equation for y:
y + 18 = 16x
Subtract 18 from both sides:
y = 16x - 18
Now that we have an expression for y, we can substitute it into the first equation:
0.5x + 0.25(16x - 18) = 36
Distribute the 0.25 to both terms inside the parentheses:
0.5x + 4x - 4.5 = 36
Combine like terms:
4.5x - 4.5 = 36
Add 4.5 to both sides:
4.5x = 40.5
Divide by 4.5:
x = 9
Now that we have the value of x, we can substitute it back into the second equation to find y:
y = 16(9) - 18
y = 144 - 18
y = 126
Therefore, the solution to the system of equations is x = 9 and y = 126.