Determine the number of solutions to a system of equations.y = -6x-2, y = -6x-2
One Solution
No Solution
Infinitely Many Solutions
y = 0.5x + 5, y = 0.5x + 1
y = 0.25x - 2. y = 5x - 4
y = 2x + 3. y = 4x -1
y = 2x + 1.5, y = 2x + 1.5
y = -x - 3y = -x + 3
Answers
y = - 6x - 2 and y = - 6x - 2 has infinitely many solutions.
y = 0.5x + 5 and y = 0.5x + 1 has no solution.
y = 0.25x - 2 and y = 5x - 4 has one solution.
y = 2x + 3 and y = 4x -1 has one solution.
y = 2x + 1.5 and y = 2x + 1.5 has infinitely many solutions.
y = -x - 3 and y = -x + 3 has has no solution.
What is a linear equation?
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
- If the slopes are different then one solution.
- If the slopes are the same but intercepts are different then no solution.
- If the slopes and intercepts are the same then infinitelymany solutions.
y = - 6x - 2 and y = - 6x - 2 has infinitely many solutions.
y = 0.5x + 5 and y = 0.5x + 1 has no solution.
y = 0.25x - 2 and y = 5x - 4 has one solution.
y = 2x + 3 and y = 4x -1 has one solution.
y = 2x + 1.5 and y = 2x + 1.5 has infinitely many solutions.
y = -x - 3 and y = -x + 3 has has no solution.
More about the linear equation link is given below.
#SPJ2
Step-by-step explanation:
When we compare 2 system of equations (of the form y = mx + c), we take note of the following things:
- If the values of m and c in both equations are the same, they have infinitely many solutions
- If only the value of m is the same, they have no solutions
- If neither is the same, they have 1 solution
Bearing this in mind, we have the following answers:
y = -6x - 2 and y = -6x - 2
=> Infinitely many solutions
y = 0.5x + 5 and y = 0.5x + 1
=> No solutions
y = 0.25x + 2 and y = 5x - 4
=> 1 solution
y = 2x + 3 and y = 4x - 1
=> 1 solution
y = 2x + 5 and y = 2x + 5
=> Infinitely many solutions
y = -x - 3 and y = -x + 3
=> No solutions
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Answer:
The solution of the given system of equation is (-4, 1)
Step-by-step explanation:
Given system of equation 5x− y = −21 and x+y= −3
We have to find the solution of the given system of equation.
Consider the
Given system of equation
5x− y = −21 .......(1)
x + y = −3 .......(2)
Adding (1) and (2) , we have,
⇒ 5x - y + (x + y ) = -21 + (-3 )
⇒ 5x - y + x + y = -21 - 3
⇒ 5x + x = -24
⇒ 6x = -24
⇒ x = -4
Substitute x = -4 in (2) , we get,
x + y = −3 ⇒ (-4) + y = −3 ⇒ y = -3 + 4 ⇒ y = 1
Thus, the solution of the given system of equation is (-4, 1)
y = 5x + 21
Substituting into:
x + y = -3
x + 5x + 21 = -3
6x = -24
x = -4
y = 5(-4) + 21
y = 1
Solution: (-4,1)