Question

Solve for x and y.
8
5
Х
15
У
12

Answer 1

From the first diagram, we can write the equation:

$x\text{ + y = 16 ----equation(1)}$

From the second diagram, we can write the equation:

$8\text{ + y = x ------equation (2)}$

Substitute the expression for x in equation (2) into equation (1)

$\begin{gathered} x\text{ + y = 16} \\ 8\text{ + y + y = 16} \\ 8\text{ + 2y = 16} \\ \text{Collect like terms} \\ 2y\text{ = 16 -8} \\ 2y\text{ = 8} \\ \text{Divide both sides by 2} \\ \frac{2y}{2}\text{ = }\frac{8}{2} \\ y\text{ = 4} \end{gathered}$

Substituting the value of y into equation (2):

$\begin{gathered} 8\text{ + y = x} \\ x\text{ = 8 + 4} \\ x\text{ = 12} \end{gathered}$

Answer:

x = 12, y = 4