For the given system of linear equations to give an infinite number of solutions the value of k should be 2.
<h3>What is a Dependent Consistent System of equations?</h3>
A system of the equation to be a Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
Given the two systems of linear equations,
2x + 3y = 4
(k+ 2)x + 6y = 3k+2
For any system of equations to have infinitely many solutions, the equation of the linear system must be in ratio, so that the lines of the equations overlap each other. Therefore, the ratio for the two of the given equations can be written as,
2/(k+2) = 3/6 = 4/(3k+2)
Solving the ratio to get the value of k,
2/(k+2) = 3/6
2/(k+2) = 1/2
2 × 2 = 1 × (k+2)
4 = k + 2
4 - 2 = k
k = 2
Hence, for the given system of linear equations to give an infinite number of solutions the value of k should be 2.
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Answer: you will have 56
Step-by-step explanation:
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Answer:
x = 7
Step-by-step explanation:
You solve a linear equation by putting the variable on one side of the equal sign and a constant on the other side. Here, variables and constants are on both sides of the equal sign, so you need to separate them.
The basic idea is that you add the opposite of any term you don't want. Whenever you perform any operation (like "add"), <em>you must do it to both sides of the equation</em>.
We observe that x-terms have coefficients of 10 and 9. We choose to add the opposite of 9x to both sides:
10 -9x -5 = 9x -9x +2
x -5 = 2 . . . . simplify
Now, we still have -5 on the left, where we don't want it. So, we add its opposite (+5) to both sides:
x -5 +5 = 2 +5
x = 7 . . . . simplify
The solution is x = 7.
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<em>Additional comment</em>
If we were to end up with an x-coefficient other than 1, we would divide both sides of the equation by that coefficient. This will leave the x-term with a coefficient of 1.
Multiply length time width, and make sure you square your answer!
