The system of equation has infinite number of solutions.
Further explanation:
Consider the first linear equation as [tex]{a_1}x + {b_1}y={c_1}.[/tex]
The second linear equation is [tex]{a_2}x + {b_2}y={c_2}.[/tex]
The conditions to check the solutions of the equations are as follows.
1. If [tex]\boxed{\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}=\frac{{{c_1}}}{{{c_2}}}}[/tex] then the equations has infinite number of solution.
2. If [tex]\boxed{\frac{{{a_1}}}{{{a_2}}}=\frac{{{b_1}}}{{{b_2}}}\ne\frac{{{c_1}}}{{{c_2}}}}[/tex] then the equations has no solution.
3. If [tex]\boxed{\frac{{{a_1}}}{{{a_2}}} \ne \frac{{{b_1}}}{{{b_2}}}}[/tex] 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, [tex]{a_1}[/tex] is equal to 3, [tex]{b_1}[/tex] is equal to 3, [tex]{c_1}[/tex] is equal to 10, [tex]{a_2}[/tex] is equal to - 9, [tex]{b_2}[/tex] is equal to -9 and [tex]{c_2}[/tex] is equal to -30.
The value of [tex]\dfrac{{{a_1}}}{{{a_2}}}[/tex] can be calculated as,
[tex]\begin{aligned}\frac{{{a_1}}}{{{a_2}}}&=\frac{3}{{ - 9}}\\\frac{{{a_1}}}{{{a_2}}}&=-\frac{1}{3}\\\end{aligned}[/tex]
The value of [tex]\dfrac{{{b_1}}}{{{b_2}}}[/tex] can be calculated as,
[tex]\begin{aligned}\frac{{{b_1}}}{{{b_2}}}&=\frac{3}{{ - 9}}\\\frac{{{b_1}}}{{{b_2}}}&= -\frac{1}{3}\\\end{aligned}[/tex]
The value of [tex]\dfrac{{{c_1}}}{{{c_2}}}[/tex] can be calculated as,
[tex]\begin{aligned}\frac{{{c_1}}}{{{c_2}}}&=\frac{10}{{ - 30}}\\\frac{{{c_1}}}{{{c_2}}}&=-\frac{1}{3}\\\end{aligned}[/tex]
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 https://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.
