Respuesta :
Answer:
Option B that is (2,6) is correct
Explanation:
We have been given with system of equations
[tex]X+Y=8[/tex] and [tex]Y=3X[/tex]
Here, we will substitute the value of [tex]Y=3X[/tex] in [tex]X+Y=8[/tex]
We will get [tex]X+3X=8[/tex]
Further simplification we will get to [tex]4X=8[/tex]
Hence, the value of [tex]X=2[/tex]
And now, substituting the value [tex]X=2[/tex] in [tex]Y=3X[/tex] we will get [tex]Y=6[/tex].
Therefore, option B is correct.
The solution set for the system of linear equations [tex]x + y = 8[/tex] and [tex]y = 3x[/tex] is [tex]\boxed{\left\{{\left({{\mathbf{2,6}}}\right)}\right\}}[/tex].
Further explanation:
It is given that the system of linear equations are [tex]x + y = 8[/tex] and [tex]y = 3x[/tex].
Consider the given equations as follows:
[tex]x + y = 8\,\,\,[/tex] ......(1)
[tex]y = 3x\,\,\,[/tex] ......(2)
From equation (2), the value of [tex]y[/tex] in terms of [tex]x[/tex] is[tex]3x[/tex].
Now, substitute [tex]3x[/tex] for [tex]y[/tex] in the equation (1) as follows:
[tex]x + 3x = 8[/tex]
The variable is eliminated in the above equation.
Simplify the equation as follows:
[tex]\begin{aligned}x + 3x&=8\\4x&=8\\x&=\frac{8}{4}\\x&=2\\\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]2[/tex].
Substitute [tex]2[/tex] for [tex]x[/tex] in the equation (2) and obtain the value of [tex]y[/tex] as shown below.
[tex]\begin{aligned}y&= 3\left( 2\right)\\&=6\\\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]6[/tex].
Thus, the ordered pair for the given system of linear equation is [tex]\left({{\mathbf{2,6}}} \right)[/tex].
Check whether the obtained solution [tex](2,6)[/tex] satisfies the given equations or not.
Substitute [tex]2[/tex] for [tex]x[/tex] and [tex]6[/tex] for [tex]y[/tex] in the equation (1) and check the equation.
[tex]\begin{aligned}2 + 6\mathop&_=^? 8\hfill \\\,\,\,\,\,\,\,8 &= 8\,\,\,\hfill\\\end{aligned}[/tex] (True)
The ordered pair [tex]\left({2,6}\right)[/tex] satisfies the equation (1).
Substitute [tex]2[/tex] for [tex]x[/tex] and [tex]6[/tex] for [tex]y[/tex] in the equation (2) and check the equation.
[tex]\begin{aligned}6\mathop&_= ^? \:3\left( 2 \right)\hfill\\6&= 6\,\,\,\,\,\,\,\,\,\,\,\,\hfill\\\end{aligned}[/tex] (True)
The ordered pair [tex]\left({2,6}\right)[/tex] satisfies the equation (2).
Thus, the solution set for the system of linear equations [tex]x + y = 8[/tex] and [tex]y = 3x[/tex] is [tex]\boxed{\left\{{\left({{\mathbf{2,6}}}\right)}\right\}}[/tex].
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Linear equations
Keywords: Substitution, linear equation, system of linear equations in two variables, variables, mathematics,[tex]x + y = 8[/tex] ,[tex]y = 3x[/tex] , solution set
