Respuesta :
Use substitution
-x + 4 = 1/3x + 8
4 = 4/3x + 8
-4 = 4/3x
x = -4 * 3/4
x = -3
Then plug x into one of the original equations. In this case y = -x + 4 is the easiest.
y = -(-3) + 4
y = 7
-x + 4 = 1/3x + 8
4 = 4/3x + 8
-4 = 4/3x
x = -4 * 3/4
x = -3
Then plug x into one of the original equations. In this case y = -x + 4 is the easiest.
y = -(-3) + 4
y = 7
The solution of the given systems [tex]y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8[/tex] is [tex]\boxed{\left( { - 3,7} \right)}[/tex]. Option (a) is correct.
Further explanation:
Given:
The system of equations is [tex]y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8.[/tex]
The options are as follows,
(a). [tex]\left( { - 3,7} \right)[/tex]
(b). [tex]\left( {0,8} \right)[/tex]
(c). [tex]\left( { 3,7} \right)[/tex]
(d). [tex]\left( {0,4} \right)[/tex]
Explanation:
The given system of equations is [tex]y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8.[/tex]
Equate the two equations to obtain the solution of the system of equation.
[tex]\begin{aligned}- x + 4 &= \frac{1}{3}x + 8\\- x - \frac{1}{3}x & 8 - 4\\\frac{{ - 3x - x}}{3} &= 4\\- 4x &= 12\\x&= - 3\\\end{aligned}[/tex]
The value of y can be obtained as follows,
[tex]\begin{aligned}y &= - \left( { - 3} \right) + 4\\&= 3 + 4\\&= 7\\\end{aligned}[/tex]
The solution of the given systems [tex]y = - x + 4{\text{ and }}y = \dfrac{1}{3}x + 8[/tex] is [tex]\boxed{\left( { - 3,7} \right)}[/tex]. Option (a) is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: system of equations, numbers,slope, slope intercept, equation, y-intercept, graph, representation, origin.
