The solution of the given systems [tex]y = x + 3{\text{ and }}y = 3x + 1[/tex] is [tex]\boxed{\left( { 1,4} \right)}[/tex]. Option (a) is correct.
Further explanation:
Given:
The system of equations is [tex]y = x + 3{\text{ and }}y = 3x + 1.[/tex]
The options are as follows,
(a). [tex]\left( { 1,4} \right)[/tex]
(b). [tex]\left( {0,3} \right)[/tex]
(c). [tex]\left( { 0,1} \right)[/tex]
(d). [tex]\left( {1,3} \right)[/tex]
Explanation:
The given system of equations is [tex]y = x + 3{\text{ and }}y = 3x + 1[/tex].
Equate the two equations to obtain the solution of the system of equation.
[tex]\begin{aligned}3x + 1 &= x + 3\\3x - x &= 3 - 1\\2x &= 2\\x &= \frac{2}{2}\\x&= 1\\\end{aligned}[/tex]
The value of [tex]y[/tex] can be obtained as follows,
[tex]\begin{aligned}y&= x + 3\\&= 1 + 3\\&= 4\\\end{aligned}[/tex]
The solution of the given systems [tex]y = x + 3{\text{ and }}y = 3x + 1[/tex] is[tex]\boxed{\left( { 1,4} \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.
