solve -15x - 2y = -31, 4x + 6y = 11 using Linear Combination Method?
x = 2
y = 1/2
now stop posting the same question 20 billion times.
To solve the system of equations using the Linear Combination Method, follow these steps:
Step 1: Express both equations in standard form (Ax + By = C).
Given equations:
-15x - 2y = -31 ...(1)
4x + 6y = 11 ...(2)
To convert equation (1) to standard form, we need to make the coefficient of x positive. Multiply the entire equation by -1:
15x + 2y = 31 ...(3)
Now, we have the following two equations in standard form:
15x + 2y = 31 ...(3)
4x + 6y = 11 ...(2)
Step 2: Choose one of the equations and multiply it by a constant such that the coefficient of either x or y will be equal in magnitude (but with opposite sign) to the coefficient in the other equation. This allows the two equations to cancel each other out.
In this case, we can multiply equation (2) by 2, which gives us:
8x + 12y = 22 ...(4)
Step 3: Add or subtract the two equations obtained from steps 2 and 1 to eliminate one variable.
Subtract equation (3) from equation (4):
(8x + 12y) - (15x + 2y) = 22 - 31
Now, simplify:
8x + 12y - 15x - 2y = 22 - 31
-7x + 10y = -9 ...(5)
Step 4: Solve the resulting equation for the remaining variable.
We have:
-7x + 10y = -9 ...(5)
To isolate y, we solve for y:
10y = 7x - 9
y = (7/10)x - 9/10 ...(6)
Step 5: Substitute the value of y (found in step 4) into any one of the original equations to solve for x.
Let's substitute equation (6) into equation (1):
-15x - 2(7/10)x + 9/10 = -31
Simplify:
-15x - (14/10)x + (9/10) = -31
-15x - (7/5)x + (9/10) = -31
-75x - 14x + 9 = -310 ...(7)
Combine like terms:
-89x + 9 = -310
Move 9 to the right side of the equation:
-89x = -310 - 9
-89x = -319
Finally, solve for x:
x = (-319) / (-89)
x = 3.59
Step 6: Substitute the value of x (found in step 5) into equation (6) to solve for y:
y = (7/10)(3.59) - 9/10
y = 2.513 - 0.9
y = 1.613
So, the solution to the system of equations is x = 3.59 and y = 1.613.