To solve the system of equations using substitution, we'll follow these steps:

The system of equations is:

1. $2x + y = 3$
2. $4x + 4y = 8$

Step 1: Solve one equation for one variable.

Let's solve the first equation $2x + y = 3$ for $y$.

$y = 3 - 2x$

Step 2: Substitute this expression for $y$ in the second equation.

Now, substitute $y = 3 - 2x$ into the second equation $4x + 4y = 8$:

$4x + 4(3 - 2x) = 8$

Step 3: Simplify and solve for $x$.

Distribute the 4:

$4x + 12 - 8x = 8$

Combine like terms:

$-4x + 12 = 8$

Subtract 12 from both sides:

$-4x = -4$

Solve for $x$:

$x = 1$

Step 4: Substitute $x = 1$ back into the equation for $y$.

Substitute $x = 1$ into the equation $y = 3 - 2x$:

$y = 3 - 2(1) = 3 - 2 = 1$

Solution:

The solution to the system of equations is $x = 1$ and $y = 1$.

Final Answer:

$(x, y) = (1, 1)$

Do you need further clarification or have any questions about the process?

Related Questions:

1. How would you solve this system using the elimination method?
2. What happens if the system of equations is inconsistent or has no solution?
3. Can substitution be used with nonlinear equations? How?
4. How do you check the solution of a system of linear equations?
5. What is the graphical interpretation of the solution to this system?

Tip:

Always ensure you check your solution by substituting the values back into both original equations. This confirms that they satisfy the system.