Solve by substitution:
x + 2y =1
8x + 8y =4
x + 2y =1 --- (1)
8x + 8y =4 --- (2)
From (1),
x + 2y = 1
x = 1 - 2y --- (3)
Sub (3) into (2),
8 (1-2y) + 8y = 4
8 - 16y + 8y = 4
-8y = 4 - 8
-8y = -4
y = -0.5
sub y = -0.5 into (3),
x = 1 - 2(-0.5)
x = 1 + 1
x = 2
CHECK: sub x = 2 and y = -0.5 into (1),
2 + 2(-0.5) = 1
To solve the system of equations by substitution, we need to isolate one variable in one equation and substitute it into the other equation. Let's solve the first equation for x:
x + 2y = 1
We can rearrange the equation to isolate x:
x = 1 - 2y
Now that we have an expression for x, we can substitute it into the second equation:
8(1 - 2y) + 8y = 4
Simplifying the equation gives us:
8 - 16y + 8y = 4
Combining like terms:
-8y + 8 = 4
Simplifying further:
-8y = 4 - 8
-8y = -4
Dividing both sides by -8:
y = -4 / -8
y = 1/2
Now that we have the value of y, we can substitute it back into the first equation to solve for x:
x + 2(1/2) = 1
x + 1 = 1
Subtracting 1 from both sides:
x = 1 - 1
x = 0
Therefore, the solution to the system of equations is x = 0 and y = 1/2.