5x-4y=-7
3x-3y=-21
(linear combination method)
Multiply Eq1 by 3 and Eq2 by -4 and add:
15x - 12y = -21
-12x + 12y = 84
Sum:3x = 63, X = 21.
In Eq1, replace x with 21 and solve for y:
15*21 - 12y =-21, 315 - 12y=-21,
-12y = -336, Y = 28.
To solve this system of equations using the linear combination method, follow these steps:
Step 1: Multiply one or both equations by a constant so that the coefficients of either x or y will cancel each other out when added or subtracted.
Let's multiply the second equation by 2 to make the coefficients of y line up:
Original equations:
5x - 4y = -7 --(1)
3x - 3y = -21 --(2)
Multiply equation (2) by 2:
6x - 6y = -42 --(3)
Step 2: Add or subtract the two equations to eliminate one variable.
Now we will subtract equation (3) from equation (1):
(5x - 4y) - (6x - 6y) = -7 - (-42)
5x - 4y - 6x + 6y = -7 + 42
-x + 2y = 35 --(4)
Step 3: Solve for one variable.
Now solve equation (4) for y:
-x + 2y = 35
2y = x + 35
y = (1/2)x + 35/2 --(5)
Step 4: Substitute the value of y obtained in equation (5) back into one of the original equations to find the value of the other variable.
Let's substitute equation (5) into equation (1):
5x - 4((1/2)x + 35/2) = -7
5x - 2x - 70 = -7
3x = 63
x = 21
Step 5: Substitute the values of x and y into one of the original equations to check if they satisfy the equation.
Let's substitute x = 21 and y = (1/2)21 + 35/2 into equation (1):
5(21) - 4((1/2)21 + 35/2) = -7
105 - 42 - 70 = -7
-7 = -7
Since both sides of the equation are equal, x = 21 and y = (1/2)21 + 35/2 are the correct solutions.
Therefore, the solution to the system of equations is x = 21 and y = (1/2)x + 35/2.