Question

What is the solution to this system of equations? x 2 y = 4. 2 x minus 2 y = 5. (3, Negative 5 and one-half) (3, one-half) no solution infinitely many solutions.

Answer 1

The solution of the equation is (3, 1/2).

We have to determine

What is the solution to this system of equations?

According to the question

The given system of the equation;

$\rm x+2y=4\\ \\ 2x-2y=5$

The standard form for linear equations in two variables is;

$\rm Ax+By = C$

On comparing equation 1 and equation 2 with the standard form we get,

$\rm a_1 = 1,\ b_1 = 2,\ c_1=4\\ \\ a_2=2, \ b_2=-2, \ c_1 = 5$

Here,

$\rm \dfrac{a_1}{a_2} = \dfrac{1}{2}\\ \\ \dfrac{b_1}{b_2} = \dfrac{-2}{2} = -1\\ \\ \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$

Here,  $\rm \dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$ so, the given system of equations has a unique solution.

Then,

The solution of the equation is;

$\rm x+2y=4\\\\2x-2y=5$

On adding both the equation;

$\rm x+2y+2x-2y=4+5\\ \\ 3x=9\\ \\ x = \dfrac{9}{3}\\ \\ x = 3$

Substitute the value of x in equation 1,

$\rm x+2y=4\\ \\ 3+2y = 4\\ \\ 2y = 4-3\\ \\ 2y=1\\ \\ y =\dfrac{1}{2}$

Hence, the solution of the equation is (3, 1/2).

To know more about System of Equation click the link given below.

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Answer 2

Answer:

(3,1/2)

Step-by-step explanation:

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