The problem asks to solve systems of linear equations using the substitution method. We will solve question 1 and question 2. Question 1: $2x + y = 5$ $x + 3y = 5$ Question 2: $x + 2y = 8$ $2x + 3y = 14$

1. Problem Description

The problem asks to solve systems of linear equations using the substitution method. We will solve question 1 and question

2.

Question 1:

$2x + y = 5$

$x + 3y = 5$

Question 2:

$x + 2y = 8$

$2x + 3y = 14$

2. Solution Steps

Question 1:

We have the system of equations:

$2x + y = 5$ (1)

$x + 3y = 5$ (2)

From equation (2), we can express $x$ in terms of $y$:

$x = 5 - 3y$ (3)

Substitute equation (3) into equation (1):

$2(5 - 3y) + y = 5$

$10 - 6y + y = 5$

$10 - 5y = 5$

$-5y = -5$

$y = 1$

Substitute $y = 1$ back into equation (3):

$x = 5 - 3(1) = 5 - 3 = 2$

So, the solution is $x = 2$ and $y = 1$.

Question 2:

We have the system of equations:

$x + 2y = 8$ (1)

$2x + 3y = 14$ (2)

From equation (1), we can express $x$ in terms of $y$:

$x = 8 - 2y$ (3)

Substitute equation (3) into equation (2):

$2(8 - 2y) + 3y = 14$

$16 - 4y + 3y = 14$

$16 - y = 14$

$-y = -2$

$y = 2$

Substitute $y = 2$ back into equation (3):

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

So, the solution is $x = 4$ and $y = 2$.

3. Final Answer

Question 1: $x = 2, y = 1$

Question 2: $x = 4, y = 2$