solve and comparison:
a)4x-9y+4
6x+15y=-13
im so lost!!!!!
srry
it's
solve and comparison:
a)4x-9y=4
6x+15y=-13
im so lost!!!!!
Help me is NOT the name of this post. Math or Algebra.
Sra
4x-9y=4
6x+15y=-13
To solve, first isolate x (or y) in one of the equations.
4x = 4 + 9y
x = 1 + 2.25y
Substitute the right hand portion for x in the second equation.
6(1 + 2.25y) + 15y = -13
Solve for y. Put that value into the first equation to solve for x. To check, put both values into the second equation.
I hope this helps. Thanks for asking.
To solve the system of equations:
a) 4x - 9y + 4 = 0
6x + 15y = -13
First, we can simplify the second equation by dividing both sides by 3:
2x + 5y = -13/3
Now, we can rewrite the system of equations in matrix form as:
[A] [X] = [B]
where [A] represents the coefficients of the variables x and y, [X] represents the variables x and y, and [B] represents the constants on the right-hand side.
The matrix form of the given system is:
[4 -9] [x] = [-4]
[2 5] [y] = [-13/3]
To solve for [X], we can use Gaussian elimination or substitution method.
Let's use substitution method:
From the first equation, we can solve for x in terms of y:
4x = 9y - 4
x = (9y - 4)/4
Now substitute this expression for x in the second equation:
2[(9y - 4)/4] + 5y = -13/3
Simplify this equation:
(9y - 4)/2 + 5y = -13/3
(9y - 4 + 10y)/2 = -13/3
(19y - 4)/2 = -13/3
Cross-multiply:
3(19y - 4) = -13(2)
57y - 12 = -26
57y = -14
y = -14/57
Substitute this value of y back into the first equation to solve for x:
4x - 9(-14/57) + 4 = 0
4x + 126/57 + 4 = 0
4x + 126/57 + 228/57 = 0
4x + 354/57 = 0
4x = -354/57
x = -354/57 * 1/4
x ≈ -3.875
Therefore, the solution to the system of equations is approximately x = -3.875 and y = -14/57.
To compare the solutions, you can substitute the values of x and y into each equation of the original system:
For the first equation: 4x - 9y + 4 = 0
Substituting x = -3.875 and y = -14/57:
4(-3.875) - 9(-14/57) + 4 ≈ 0
-15.5 + 22/19 + 4 ≈ 0
-8.6667 + 1.1579 + 4 ≈ 0
-8.6667 + 1.1579 + 4 ≈ 0
Approximately 0 ≈ 0 (which is true)
For the second equation: 6x + 15y = -13
Substituting x = -3.875 and y = -14/57:
6(-3.875) + 15(-14/57) = -13
-23.25 - 210/57 = -13
-23.25 - 3.6842 ≈ -13
Approximately -26.9342 ≈ -13 (which is true)
Since both equations are satisfied by the values of x and y we obtained, we can conclude that the solution is correct.
I hope this explanation helps you understand how to solve and compare the given system of equations.