6x=9y-21. 6y=4x+14
plz help...I can't figure out how to do this problem using linear equations with two variables
Eq1: 6x - 9y = -21.
Eq2: 4x - 6y = -14.
Divide both sides of Eq1 by 3 , and divide both sides of Eq2 by 2:
2x - 3y = -7.
2x - 3y = -7.
The 2 Eqs are identical and represent the same line. Therefore, we have an
infinite # of solutions.
what is .5 cubed?
To solve this system of linear equations, we can use one of several methods, such as substitution or elimination. Let's use the elimination method.
First, we'll start by rearranging the equations to isolate one variable. Let's rearrange the first equation to isolate the variable x:
6x = 9y - 21
Divide both sides of the equation by 6:
x = (9y - 21)/6
Now, let's rearrange the second equation to isolate the variable y:
6y = 4x + 14
Divide both sides of the equation by 6:
y = (4x + 14)/6
Now, we have the following two equations:
x = (9y - 21)/6
y = (4x + 14)/6
Next, we'll substitute the expression for x in terms of y into the second equation:
y = (4((9y - 21)/6) + 14)/6
Simplify this equation step by step:
1. Multiply 4 by (9y - 21):
y = (36y - 84 + 14)/6
2. Combine like terms on the right side of the equation:
y = (36y - 70)/6
Next, multiply every term in the equation by 6 to clear the fraction:
6y = 36y - 70
Now, let's isolate the variable y on one side of the equation by moving all y terms to the left side and all constant terms to the right side:
36y - 6y = 70
Simplify:
30y = 70
Divide both sides of the equation by 30 to solve for y:
y = 70/30
Simplify:
y = 7/3 or y = 2.33
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
6x = 9y - 21
Substitute y = 7/3:
6x = 9(7/3) - 21
Multiply 9 by (7/3):
6x = 21 - 21
Simplify:
6x = 0
Divide both sides of the equation by 6 to solve for x:
x = 0/6
Simplify:
x = 0
So, the solution to the system of equations is x = 0 and y = 7/3 (or y = 2.33).
To solve this system of linear equations with two variables, we can use the method of substitution or elimination. Let's start with the substitution method:
1. Given equations:
Equation 1: 6x = 9y - 21
Equation 2: 6y = 4x + 14
2. Solve one equation for one variable. Let's solve Equation 2 for y:
Equation 2: 6y = 4x + 14
Divide both sides by 6:
6y/6 = (4x + 14)/6
y = (2/3)x + 7/3
3. Substitute the expression for y from Equation 2 into Equation 1:
Equation 1: 6x = 9y - 21
Substitute y with (2/3)x + 7/3:
6x = 9((2/3)x + 7/3) - 21
4. Simplify and solve for x:
Distribute 9 to (2/3)x and 7/3:
6x = 6x + 42/3 - 21
Simplify:
6x = 6x + 14 - 21
Combine like terms:
6x - 6x = -7
0 = -7
5. The equation 0 = -7 is not true, which means there is no solution to this system of equations. The two lines represented by the equations are parallel and will never intersect.
Therefore, the system of equations is inconsistent, and there is no solution.