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mylen [45]
3 years ago
14

What is the solution of this system of linear equations? 3y = 3 y equals StartFraction 3 over 2 EndFraction x plus 6.X + 6 y – S

tartFraction one-half EndFraction y minus StartFraction 1 over 4 EndFraction x equals 3.X = 3 (3, 6) (2, 1) no solution infinite number of solutions
Mathematics
2 answers:
Gennadij [26K]3 years ago
6 0

The solution of the given system of equation is \boxed{\bf (0,6)}.

Further explanation:

The given system of equations is as follows:

\boxed{\begin{aligned}y&=\dfrac{3}{2}x+6\\ \dfrac{y}{2}-\dfrac{x}{4}&=3\end{aligned}}

Label the above equations as follows:

y&=\dfrac{3}{2}x+6                                      ......(1)

\dfrac{y}{2}-\dfrac{x}{4}&=3                         ......(2)

To obtain the solution of the given system of equation use the substitution method.

Substitute the expression y&=\frac{3}{2}x+6 in equation (2) to obtain the value of x.

\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}

Therefore, the value of x is 0.

Substitute 0 for x in equation (1) to obtain the value of y.

\begin{aligned}y&=\left(\dfrac{3}{2}\cdot 0\right)+6\\&=6\end{aligned}

Therefore, the value of y is 6.

From the above calculation it is concluded that the solution of the given system of equation is (0,6).

Thus, the solution of the given system of equation is \boxed{\bf (0,6)}.

Learn more:

1. A problem on composite function brainly.com/question/2723982  

2. A problem to find radius and center of circle brainly.com/question/9510228  

3. A problem to determine intercepts of a line brainly.com/question/1332667  

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.

Scrat [10]3 years ago
3 0

Answer:

(0,6)

Step-by-step explanation:

The given system of equations is

y =  \frac{3}{2}x + 6

and

\frac{1}{2}y -  \frac{1}{4}x = 3

We substitute the first equation into the second equation to get:

\frac{1}{2} ( \frac{3}{2}x + 6) -  \frac{1}{4}x = 3

We expand to get:

\frac{3}{4} x + 3 -  \frac{1}{4}x = 3

We group similar terms to get:

\frac{3}{4}x -  \frac{1}{4}x = 3 - 3

\frac{1}{2}x = 0

x = 0

Put x=0 in to the first equation to get:

y = 6

Therefore the solution is (0,6)

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