Question

Solve system of equations using the method of substitution. Identify wether the system represents parallel, coincident, or parallel lines.5x+2y=167.5x+3y=24

Answer 1

Given

5x+2y=16 ---(1)

7.5x+3y=24 ----(2)

Find

1) value of x and y

2) Type of system

Step-by-step explanation

From equation (1)

`\begin{gathered} 5x+2y=16 \\ 5x=16-2y \\ x=(16-2y)/(5) \end{gathered}`

Putting this value of x in equation 2

`\begin{gathered} 7.5x+3y=24 \\ 7.5((16-2y)/(5))+3y=24 \\ 1.5(16-2y)+3y=24 \\ 24-3y+3y=24 \end{gathered}`

From here we cannot find the values of x and y as 3y and -3y will cancel each other. Hence there is not a particular solution

Checking the type of system

From these equations we get

`(a1)/(a2)=(b1)/(b2)=(c1)/(c2)`

Therefore the lines are coincident to each other

Therefore the lines have infinte solutions

Final Answer

Therefore the lines have infinte solutions

The lines are coincident to each other