All categories

3 years ago

How many solutions does the system of equations below have? y=3x+4 y+6x=3x

Mathematics

1 answer:

koban [17]3 years ago

7 0

Answer:

x = - $\frac{2}{3}$

y = 2

Step-by-step explanation:

The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations such that one of the variables shared between the two equations has the inverse coefficient of the same variable in the other equation. Therefore, when one adds the equations, the variable cancels. One can solve for the variable using inverse operations, and then backsolve to find the value of the first variable.

When given the following system:

y = 3x + 4

y + 6x = 3x

Use inverse operations so that both equations are solve for one variable,

y = 3x + 4

y = -3x

Add the systems so that one of the variables (x) cancels, this process is called the process of elimination;

y = 3x + 4

y = -3x

_________

2y = 4

Inverse operations,

2y = 4

y = 2

Now backsolve, find the value of (x) by substituting the value of (y) into the equation:

y = -3x

2 = -3x

x = - $\frac{2}{3}$

You might be interested in

Blank 1 - 2850342043504625 Blank 2. - 20253035Blank 3 4350462550755225 Blank 4 20253035

Lunna [17]

The determinant of the matrix for the pineapple cake is 4350

The price of a pineapple cake is $30

The determinant of the matrix for the chocolate cake is 5075

The price of a chocolate cake is $35

Basically, what we want to do in this question is to form a set of linear equations then use matrix determinant method to solve for the unknowns in the linear equation.

Before we set up these equations,we need to use variables to represent the fruit prices;

Let p represent the price a of pineapple

Let c represent the price of a chocolate;

So let us proceed to form the linear equations;

The equation for the weekdays sales will be;

$45p\text{ + 62c = 3520}$

The equation for the weekend sales will be;

$55p\text{ + 79c = }4415$

Now, we have two equations that we need to use the matrix determinant method to solve;

$\begin{bmatrix}{45} & {62} \\ {55} & {79} \\ {} & {}\end{bmatrix}\text{ }\begin{bmatrix}{p} & \\ {c} & {} \\ {} & \end{bmatrix}\text{ = }\begin{bmatrix}{3520} & {} & \\ {4415} & {} & \\ {} & {} & \end{bmatrix}$

The above is the matrix set up we wil use;

Now, we start by calculating the determinant of 2 * 2 matrix; that would be;

$\begin{gathered} \Delta\text{ = (45 }\times\text{ 79) - (62 }\times\text{ 55)} \\ \Delta\text{ = 3555-3410 = 145} \end{gathered}$

Next is to find the determinant of the pineapple cake matrix;

To find this, what we will do is to substitute the coefficient of p with the total sales value to get a new matrix set;

The matrix for the pineapple cake will be;

$\begin{gathered} \begin{bmatrix}{3520} & {62} \\ {4415} & {79} \\ {} & {}\end{bmatrix}\text{ } \\ \\ \text{The }\det er\min ant\text{ here will be ;} \\ \Delta_{p\text{ = }}(3520\text{ }\times\text{ 79) - (62 }\times\text{ 4415)} \\ =\text{ 4350} \end{gathered}$

Next is to find the determinant of the chocolate cake matrix;

To find this, what we will do is to substitute the coefficient of c with the total sales value to get a new matrix set;

The matrix for the chocolate cake will be;

$\begin{gathered} \begin{bmatrix}{45} & {3520} \\ {55} & {4415} \\ {} & {}\end{bmatrix} \\ \\ \Delta_c\text{ = (45 }\times\text{ 4415) - (55 }\times\text{ 3520)} \\ =\text{ 5075} \end{gathered}$

Finally, we proceed to get the prices for the pineapple and the cake;

To get this, we simply divide the matrix of each by the initial matrix value;

$\begin{gathered} p\text{ = }\frac{\Delta_p}{\Delta}=\frac{4350}{145}=30_{} \\ \\ c\text{ = }\frac{\Delta_c}{\Delta}\text{ = }\frac{5075}{145}\text{ = 35} \end{gathered}$

6 0

1 year ago

Please help with the question below

Oksanka [162]

There is no answer below

3 0

4 years ago

Use the exponent properties to simplify the following<br> <img src="https://tex.z-dn.net/?f=%5Cfrac%7B3x%5E3y%5E2z%7D%7B27xy%5E2

7nadin3 [17]

Step-by-step explanation:

x^2/9 z^2

hiiii checkout the steps