Need help to solve can anyone help me please 6x-9y = 25.5 7y-2x =-10.0 solve the elimination method
Eq1: 6X - 9Y = 25.5,
Eq2: -2x + 7y = -10.
Multiply Eq2 by 3:
6X - 9Y = 25.5.
-6X + 21Y = -30.
Sum: 12y = - 4.5,
Y = 0.375.
In Eq2, substitute 0.375 for y:
-2X + 7*0.375 = - 10,
-2X = -10 -0.375 = -10.375,
X = 5.1875.
Solution Set: (x,y) = (5.1875,0.375).
CORRECTION:
In Eq2, substitute 0.375 for y:
-2X + 7*0.375 = -10,
-2X + 2.625 = -10,
-2X = -10 - 2.625 = -12.625.
X = 6.3125.
Solution Set: (x,y) = (6.3125,0.375).
=
Sure, I can help you solve the system of equations using the elimination method.
Step 1: Multiply the two equations by appropriate numbers to make the coefficients of either x or y in both equations the same (but with opposite signs).
Let's start with multiplying the first equation by 2 and the second equation by 3, so that the coefficients of x are opposites of each other:
Equation 1: 2(6x - 9y) = 2(25.5) becomes 12x - 18y = 51
Equation 2: 3(7y - 2x) = 3(-10.0) becomes 21y - 6x = -30
Step 2: Add the two equations together, eliminating the x variable.
Add Equation 1 and Equation 2:
(12x - 18y) + (21y - 6x) = 51 + (-30)
Combine like terms:
12x - 6x - 18y + 21y = 51 - 30
6x + 3y = 21
Step 3: Simplify Equation 3 to get the value of one variable (either x or y).
6x + 3y = 21
Divide the entire equation by 3:
(6x + 3y) / 3 = 21 / 3
This simplifies to:
2x + y = 7
Now we have a simplified equation.
Step 4: Solve Equation 4 by isolating one variable.
Let's isolate y:
2x + y = 7
Subtract 2x from both sides:
y = 7 - 2x
Step 5: Substitute the value of y into one of the original equations to find the value of the other variable.
Let's substitute the value of y into Equation 1:
6x - 9y = 25.5
6x - 9(7 - 2x) = 25.5
6x - 63 + 18x = 25.5
Combine like terms:
24x - 63 = 25.5
Add 63 to both sides:
24x = 25.5 + 63
24x = 88.5
Divide both sides by 24:
x = 88.5 / 24
x ≈ 3.69
Step 6: Substitute the value of x into either Equation 1 or Equation 2 to find the value of y.
Let's substitute the value of x into Equation 2:
7y - 2x = -10.0
7y - 2(3.69) = -10.0
7y - 7.38 = -10.0
Add 7.38 to both sides:
7y = -10 + 7.38
7y = -2.62
Divide both sides by 7:
y = -2.62 / 7
y ≈ -0.37
Therefore, the solution to the system of equations is approximately x = 3.69 and y = -0.37.