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} \\ (2y)/(2)\text{ = }(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