Question

A student bought a calculator and a textbook for a course in algebra. He told his friend that the total cost was $130(without tax) and that the calculator cost $30 more than thrice the cost of the textbook. What was the cost of eachitem? Let x = the cost of a calculator and y = the cost of the textbook. The corresponding modeling system isS x + y = 130Solve the system by using the method of substitution.x = 3y + 30

Answer 1

Gievn equations are,

`\begin{gathered} x+y=130\ldots(1) \\ x=3y+30\ldots(2) \end{gathered}`

To solve the equation using subsitution method,

Substitute, equation (2) in (1)

`\begin{gathered} 3y+30+y=130 \\ 4y+30=130 \\ 4y=130-30 \\ 4y=100 \\ y=(100)/(4) \\ y=25 \end{gathered}`

put y =25 in equation (2)

`\begin{gathered} x=3\cdot\: 25+30 \\ x=75+30 \\ x=105 \end{gathered}`

the solution to the given system of equation are,

`(x,y)=(105,25)`