Respuesta :
Answer:
(0,6)
Step-by-step explanation:
The given system of equations is
[tex]y = \frac{3}{2}x + 6[/tex]
and
[tex] \frac{1}{2}y - \frac{1}{4}x = 3[/tex]
We substitute the first equation into the second equation to get:
[tex] \frac{1}{2} ( \frac{3}{2}x + 6) - \frac{1}{4}x = 3[/tex]
We expand to get:
[tex] \frac{3}{4} x + 3 - \frac{1}{4}x = 3 [/tex]
We group similar terms to get:
[tex] \frac{3}{4}x - \frac{1}{4}x = 3 - 3[/tex]
[tex] \frac{1}{2}x = 0[/tex]
[tex]x = 0[/tex]
Put x=0 in to the first equation to get:
[tex]y = 6[/tex]
Therefore the solution is (0,6)
The solution of the given system of equation is [tex]\boxed{\bf (0,6)}[/tex].
Further explanation:
The given system of equations is as follows:
[tex]\boxed{\begin{aligned}y&=\dfrac{3}{2}x+6\\ \dfrac{y}{2}-\dfrac{x}{4}&=3\end{aligned}}[/tex]
Label the above equations as follows:
[tex]y&=\dfrac{3}{2}x+6[/tex] ......(1)
[tex]\dfrac{y}{2}-\dfrac{x}{4}&=3[/tex] ......(2)
To obtain the solution of the given system of equation use the substitution method.
Substitute the expression [tex]y&=\frac{3}{2}x+6[/tex] in equation (2) to obtain the value of [tex]x[/tex].
[tex]\begin{aligned}\dfrac{1}{2}\left(\dfrac{3}{2}x+6\right)-\dfrac{x}{4}&=3\\\dfrac{3}{4}x+3-\dfrac{x}{4}&=3\\\dfrac{3x-x}{4}+3-3&=0\\\dfrac{2x}{4}&=0\\x&=0\end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]0[/tex].
Substitute [tex]0[/tex] for [tex]x[/tex] in equation (1) to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}y&=\left(\dfrac{3}{2}\cdot 0\right)+6\\&=6\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]6[/tex].
From the above calculation it is concluded that the solution of the given system of equation is [tex](0,6)[/tex].
Thus, the solution of the given system of equation is [tex]\boxed{\bf (0,6)}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear equation
Keywords: Equation, linear equation, degree 1, higest power 1, system of linear equation, solution set, solution, mathematics, substitution method, consistent system , inconsistent system.
