what is the solution of the following linear system?
2y + 6x = -24
y - 13x = -12
a) (0,-12)
b) none
c) (0,3)
d) infinite number of solutions
and the answer i picked i was a
thanks!!!!!!!!!!!
a) is correct, the point satisfies both equations
To find the solution of the given linear system, we can use the method of substitution or elimination. Let's solve it using the elimination method:
Given:
2y + 6x = -24 ...(1)
y - 13x = -12 ...(2)
Step 1: Multiply equation (2) by 2 to make the coefficients of "y" the same in both equations:
2(y - 13x) = 2(-12)
2y - 26x = -24 ...(3)
Step 2: Add equation (1) and equation (3) to eliminate "y":
(2y + 6x) + (2y - 26x) = -24 + (-24)
4y - 20x = -48
Simplifying the equation further:
4y - 20x = -48
Divide the equation by 4 to simplify it:
y - 5x = -12 ...(4)
Step 3: Rearrange equation (4) to solve for "y":
y = 5x - 12 ...(5)
Step 4: Substitute the value of "y" from equation (5) into equation (1) or (2) to solve for "x". Let's use equation (1) to find the value of "x":
2(5x - 12) + 6x = -24
10x - 24 + 6x = -24
16x - 24 = -24
16x = 0
x = 0
Step 5: Substitute the value of "x" into equation (5) to find the value of "y":
y = 5(0) - 12
y = -12
Therefore, the solution to the linear system is (0, -12).
Hence, the correct answer is option a) (0, -12).
If you have any further questions, feel free to ask!
To solve the given linear system of equations:
2y + 6x = -24 ---- (Equation 1)
y - 13x = -12 ---- (Equation 2)
We can use the method of substitution or elimination.
Let's use the elimination method:
1. Multiply Equation 2 by 6 to make the coefficients of 'x' in both equations cancel each other out:
6(y - 13x) = 6(-12)
6y - 78x = -72 ---- (Equation 3)
Now, we have:
2y + 6x = -24 ---- (Equation 1)
6y - 78x = -72 ---- (Equation 3)
2. Multiply Equation 1 by 3 to make the coefficients of 'x' in both equations cancel each other out:
3(2y + 6x) = 3(-24)
6y + 18x = -72 ---- (Equation 4)
Now, we have:
6y + 18x = -72 ---- (Equation 4)
6y - 78x = -72 ---- (Equation 3)
3. Subtract Equation 4 from Equation 3:
(6y - 78x) - (6y + 18x) = -72 - (-72)
This simplifies to:
-96x = 0
4. Divide both sides of the equation by -96:
x = 0
5. Substitute the value of x = 0 back into either Equation 1 or Equation 2.
Using Equation 2:
y - 13(0) = -12
y = -12
6. Therefore, the solution to the given linear system of equations is (x, y) = (0, -12).
Comparing this solution to the provided answer options, you correctly chose option a) (0, -12). Well done!