Question

What is the solution of the following system 3x+3y=10 -9x-9y=-30

Answer 1

The system of equation has infinite number of solutions.

Further explanation:

Consider the first linear equation as ${a_1}x + {b_1}y={c_1}.$

The second linear equation is ${a_2}x + {b_2}y={c_2}.$

The conditions to check the solutions of the equations are as follows.

1. If $\boxed{\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}=\frac{{{c_1}}}{{{c_2}}}}$ then the equations has infinite number of solution.

2. If $\boxed{\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}\ne\frac{{{c_1}}}{{{c_2}}}}$ then the equations has no solution.

3. If $\boxed{\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}}$ then the equations has only one solution.

Given:

The equations are   3x + 3y = 10 and - 9x - 9y =  - 30.

Explanation:

The given system of equations are 3x + 3y = 10 and - 9x - 9y =  - 30.

Here, ${a_1}$ is equal to 3, ${b_1}$ is equal to 3, ${c_1}$ is equal to 10, ${a_2}$ is equal to - 9, ${b_2}$ is equal to -9 and ${c_2}$ is equal to -30.

The value of $\dfrac{{{a_1}}}{{{a_2}}}$ can be calculated as,

$\begin{aligned}\frac{{{a_1}}}{{{a_2}}}&=\frac{3}{{ - 9}}\\\frac{{{a_1}}}{{{a_2}}}&=-\frac{1}{3}\\\end{aligned}$

The value of $\dfrac{{{b_1}}}{{{b_2}}}$ can be calculated as,

$\begin{aligned}\frac{{{b_1}}}{{{b_2}}}&=\frac{3}{{ - 9}}\\\frac{{{b_1}}}{{{b_2}}}&= -\frac{1}{3}\\\end{aligned}$

The value of $\dfrac{{{c_1}}}{{{c_2}}}$ can be calculated as,

$\begin{aligned}\frac{{{c_1}}}{{{c_2}}}&=\frac{10}{{ - 30}}\\\frac{{{c_1}}}{{{c_2}}}&=-\frac{1}{3}\\\end{aligned}$

Hence, the system of equation has infinite number of solutions.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Number System

Keywords: property, zero, eight, sum, addition, identity, shows, subtraction, number sentence, division, multiplication, variables, parenthesis, exponents.

Answer 2

we have

$3x+3y=10$ --------> equation $1$

$-9x-9y=-30$ --------> equation $2$

Multiply equation $1$ by $-3$ both sides

$-3*(3x+3y)=-3*10$ -------> $-9x-9y=-30$

the two equations of the system are the same, both equations represent the same line

so

If a consistent dependent system that has an infinite number of solutions

therefore

the answer is

The system has infinite number of solutions