The system of linear equations are 5x+8y = 115 and 3x+5y = 70.
The cost of each table (x) is $15 and cost of each chair is $5.
What is system of linear equations?
"A system of linear equations is a collection of one or more linear equations involving the same set of variables. For example, is a system of three equations in the three variables x, y, z."
Let x be the cost of each table and y be the cost of each chair
According to the question,
Five small tables with eight chairs cost $115
We can write an equation
5x+8y = 115..................(1)
Next, three small tables and five chairs cost $70
we can write an equation
3x+5y = 70...................(2)
We have two equations and two unknowns (x and y)
Solving 5x+8y = 115
⇒ [tex]x = \frac{(115-8y)}{5}[/tex]
Substitute x in equation (2)
⇒ [tex]3.\frac{(115-8y)}{5} +5y = 70[/tex]
⇒ [tex]3.\frac{115}{5}-\frac{3.8}{5} y+5y = 70[/tex]
⇒ [tex]69-\frac{24}{5}y+5y = 70[/tex]
⇒ [tex]\frac{(-24y+25y)}{5} = 70-69[/tex]
⇒ [tex]\frac{1}{5}.y = 1[/tex]
⇒ y = $5
Substitute y = $5 in x
⇒ [tex]x = \frac{(115-8y)}{5}[/tex]
⇒ [tex]x = \frac{(115-8(5))}{5}[/tex]
⇒ x = $15
Hence, the system of linear equations are 5x+8y = 115 and 3x+5y = 70
The cost of each table (x) is $15 and cost of each chair is $5.
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