How do you do:4x-6y-3=7x+2y-4=-2x+3y+24
Thankyou
4 x - 6 y - 3 = 7 x + 2 y - 4 Subtract 4 x to both sides
4 x - 6 y - 3 - 4 x = 7 x + 2 y - 4 - 4 x
- 6 y - 3 = 3 x + 2 y - 4 Add 3 to both sides
- 6 y - 3 + 3 = 3 x + 2 y - 4 + 3
- 6 y = 3 x + 2 y - 1 Subtract 2 y to both sides
- 6 y - 2 y = 3 x + 2 y - 1 - 2 y
- 8 y = 3 x - 1 Divide both sides by - 8
- 8 y / ( - 8 ) = 3 x / ( - 8 ) - 1 / ( - 8 )
y = - ( 3 / 8 ) x + 1 / 8
7 x + 2 y - 4 = - 2 x + 3 y + 24 Add 2 x to both sides
7 x + 2 y - 4 + 2 x = - 2 x + 3 y + 24 + 2 x
9 x + 2 y - 4 = 3 y + 24 Subtract 2 y to both sides
9 x + 2 y - 4 - 2 y = 3 y + 24 - 2 y
9 x - 4 = y + 24 Add 4 to both sides
9 x - 4 + 4 = y + 24 + 4
9 x = y + 28 Subtract 28 to both sides
9 x - 28 = y + 28 - 28
9 x - 28 = y
y = 9 x - 28
y = y
9 x - 28 = - ( 3 / 8 ) x + 1 / 8 Multiply both sides by 8
9 x * 8 - 28 * 8 = - ( 3 / 8 ) x * 8 + ( 1 / 8 ) * 8
72 x - 224 = - 3 x + 1 Add 3 x to both sides
72 x - 224 + 3 x = - 3 x + 1 + 3 x
75 x - 224 = 1 Add 24 to both sides
75 x - 224 + 224 = 1 + 224
75 x = 225 Divide both sides by 75
x = 225 / 75 = 3
y = 9 x - 28 = 9 * 3 - 28 = 27 - 28 = - 1
The solutions are :
x = 3 , y = - 1
You can write the solutions like ( 3 , - 1 )
To solve the given system of equations:
4x - 6y - 3 = 7x + 2y - 4 = -2x + 3y + 24,
you can use the method of elimination or substitution.
1. Elimination Method:
In this method, we'll eliminate one variable at a time by adding or subtracting the equations.
Step 1: Let's start by eliminating the variable 'x'.
From equations (1) and (2), we have:
4x - 6y - 3 = 7x + 2y - 4
Rearranging this equation, we get:
4x - 7x = 6y + 2y - 3 + 4
-3x = 8y - 7
Step 2: Now, let's eliminate the variable 'y'.
From equations (2) and (3), we have:
7x + 2y - 4 = -2x + 3y + 24
Rearranging this equation, we get:
-7x - 2x = -2y - 3y + 24 + 4
-9x = -5y + 28
Step 3: Now, we have two equations:
-3x = 8y - 7 (equation 4)
-9x = -5y + 28 (equation 5)
To eliminate 'y', we can multiply equation 4 by 5 and equation 5 by 8, then subtract them:
-15x = 40y - 35 (equation 6)
-72x = -40y + 224 (equation 7)
Adding equations 6 and 7, we get:
-15x - 72x = 40y - 35 - 40y + 224
-87x = 189
Divide both sides by -87:
x = -189 / -87
x = 2.17 (rounded to two decimal places)
Step 4: Substitute the value of x back into any of the original equations. Let's use equation 1:
4x - 6y - 3 = 7x + 2y - 4
Substituting x = 2.17, we get:
4(2.17) - 6y - 3 = 7(2.17) + 2y - 4
Simplifying this equation, we can solve for y:
8.68 - 6y - 3 = 15.19 + 2y - 4
5.68 - 6y = 2y + 11.19
Move all the terms containing y to one side:
5.68 - 2y - 11.19 = 6y
-5.51 = 8y
Divide both sides by 8:
y = -5.51 / 8
y = -0.69 (rounded to two decimal places)
So, the solution to the system of equations is:
x = 2.17
y = -0.69
You can plug in these values into the original equations to verify if they satisfy all of them.