PLEASE!!!!i need help on these 4:
*4y=15-3x
2y=3x+21
*4x=5y-14
y=-6x-9
*5x=4y-30
2x=3y=-12
*2/3y=10+4x
5x=1/3y-8
use linear combinations to solve the system of linear equations
thank you!!!
4y=15-3x ...(1)
2y=3x+21 ...(2)
Rewrite in standard form:
3x+4y-15=0....(1a)
3x-2y+21=0....(2a)
Subtract 2a from 1a to get
0x+6y - 36 = 0
from which y=6
Add 2(2a) to (1a) to get
9x+0y+27 = 0
from which x = -3
Check:
4y=24, 15-3x=24 OK
2y=12, 3x+21=12 OK
You can proceed the same way for the remaining problems. Post for answer verification if you wish, but it should not be necessary because a check with the original equations should have been done as in the example.
To solve systems of linear equations using linear combinations, follow these steps:
Step 1: Choose two equations and decide which variable to eliminate first. Look for a variable that has the same coefficient but opposite signs in both equations.
Step 2: Multiply one or both equations by a constant to make the coefficients of the selected variable the same, but with opposite signs. This will allow you to add or subtract the equations and eliminate that variable.
Step 3: Add or subtract the equations to eliminate the selected variable. This will result in a new equation with only one variable.
Step 4: Solve the new equation to find the value of the remaining variable.
Step 5: Substitute the found value back into one of the original equations to solve for the other variable.
Let's apply these steps to your given systems of equations:
For the first set of equations:
Equation 1: 4y = 15 - 3x
Equation 2: 2y = 3x + 21
To eliminate y, we'll multiply Equation 2 by 2:
2(2y) = 2(3x + 21)
4y = 6x + 42
Now, let's subtract Equation 1 from this new equation:
4y - 4y = (6x + 42) - (15 - 3x)
0 = 9x + 27
Simplifying further, we get:
9x = -27
Dividing both sides of the equation by 9, we find:
x = -3
Now substitute this value back into either Equation 1 or Equation 2. Let's use Equation 2:
2y = 3(-3) + 21
2y = -9 + 21
2y = 12
Dividing both sides by 2, we find:
y = 6
So the solution for this set of equations is x = -3, y = 6.
Repeat these steps for the remaining three sets of equations and you'll find the solutions for each set.