The given equations have infinitely many solutions.
What is an equation?
- An equation is a mathematical statement which equate two algebraic expressions. An equation has an equal to (=) sign in between the expression.
- If there are two equations ax + by + c = 0 , dx + ey + f = 0 and if [tex]\frac{a}{d}= \frac{b}{e} = \frac{c}{f}[/tex] , then the equations are said to have infinite solutions.
How to know how many solutions does the system of equations have ?
The given equations are y= -2x +9 and 6x + 3y =27
Comparing with the standard equations we can see that,
- a = 2
- b = 1
- c = -9
- d = 6
- e = 3
- f = -27
∴ [tex]\frac{a}{d} =\frac{2}{6} = \frac{1}{3}[/tex]
∴ [tex]\frac{b}{e} = \frac{1}{3}[/tex]
∴ [tex]\frac{c}{f} = \frac{-9}{-27}= \frac{1}{3}[/tex]
∴ The conditions of [tex]\frac{a}{d}= \frac{b}{e} = \frac{c}{f}[/tex] is satisfied and hence the equations have infinitely many solutions.
Find more about "Solutions of Equations" here: https://brainly.com/question/2226590
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