Solve the system of liner equations -3x-4y=-23 and 3x-5y=5
To solve the system of linear equations, we can use either substitution or elimination method.
Let's use the substitution method:
Step 1: Solve one equation for one variable in terms of the other variable.
From the first equation, we can solve for x:
-3x - 4y = -23
-3x = -23 + 4y
x = (4y - 23)/-3
Step 2: Substitute this expression for x into the second equation.
3x - 5y = 5
3((4y - 23)/-3) - 5y = 5
(4y - 23) - 5y = 5
-23 -y = 5
- y = 5 + 23
- y = 28
y = -28
Step 3: Substitute the value of y back into the first equation to find x.
-3x - 4(-28) = -23
-3x + 112 = -23
-3x = -23 - 112
-3x = -135
x = -135/-3
x = 45
Therefore, the solution to the system of linear equations is x = 45 and y = -28.
To solve the system of linear equations, we can use the method of elimination.
Step 1: Multiply the second equation by -1 to eliminate the "3x" terms:
-1*(3x-5y) = -1*5
-3x + 5y = -5
Step 2: Add the modified second equation to the first equation:
(-3x - 4y) + (-3x + 5y) = (-23) + (-5)
-6x + y = -28
Now we have a new equation: -6x + y = -28.
Step 3: Solve for y in terms of x:
y = 6x - 28
Step 4: Substitute the value of y back into the first equation:
-3x - 4(6x - 28) = -23
-3x - 24x + 112 = -23
-27x = -135
x = 5
Step 5: Substitute the value of x back into the equation y = 6x - 28:
y = 6(5) - 28
y = 2
Therefore, the solution to the system of linear equations is x = 5 and y = 2.
To solve the system of linear equations -3x - 4y = -23 and 3x - 5y = 5, we can use the method of elimination.
Step 1: Multiply one or both equations by suitable constants so that the coefficients of the x's or the y's will cancel each other out when the equations are added or subtracted.
Let's multiply the first equation by 3 and the second equation by -3, so that the x-terms will cancel each other out when we add the equations:
-3 * (-3x - 4y) = -3 * (-23)
3 * (3x - 5y) = 3 * 5
This simplifies the equations to:
9x + 12y = 69
-9x + 15y = 15
Step 2: Add the two new equations together to eliminate the x-term:
(9x + 12y) + (-9x + 15y) = 69 + 15
9x - 9x + 12y + 15y = 69 + 15
27y = 84
Step 3: Solve for y by dividing both sides of the equation by 27:
27y/27 = 84/27
y = 84/27
y = 2.67 (rounded to two decimal places)
Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
-3x - 4(2.67) = -23
-3x - 10.68 = -23
-3x = -23 + 10.68
-3x = -12.32
Step 5: Solve for x by dividing both sides of the equation by -3:
-3x / -3 = -12.32 / -3
x = 4.1067 (rounded to four decimal places)
Therefore, the solution to the system of linear equations is x = 4.1067 and y = 2.67.