Respuesta :
The solution to the system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).
What is the system of equations ?
A system of equations is a collection of two or more equations with a same set of unknowns.
What is a Subsitution method ?
The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.
The given system of linear equations are :
y = 1/3x - 10 and 2x + y = 4
On solving two equations by using substitution method, It is given that
[tex]y = \frac{1}{3}x-10[/tex] … (1)
2x + y = 4 … (2)
Substituting (1) in (2)
⇒ [tex]2x + (\frac{1}{3}x-10) = 4[/tex]
By further calculation
⇒ [tex]2x + \frac{1}{3}x - 10 = 4[/tex]
⇒ [tex]2x + \frac{1}{3} x = 4 + 10[/tex]
⇒ [tex]2x + \frac{1}{3} x = 14[/tex]
Taking LCM
⇒ [tex]\frac{(6+1)}{3}x = 14[/tex]
⇒ [tex]\frac{7}{3}x = 14[/tex]
By cross multiplication
⇒ 7x = 14 × 3
⇒ 7x = 42
Divide both sides by 7
⇒ x = 6
Substitute the value of x in equation (1)
[tex]\Rightarrow\ y = (\frac{1}{3} \times (6) - 10)[/tex]
So we get
⇒ y = (2-10)
⇒ y = -8
Therefore, the solution to the system of equations is (6, -8).
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