Question

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 – StartFraction 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

Answer 1

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 $\boxed{\bf (0,6)}$.

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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.

Answer 2

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)