2x - 3y = 4
x + 4y = 3
Write the augmented matrix:
2 -3 4
1 4 3
Multiply the first row by 1/2:
1 -3/2 2
1 4 3
Subtract the second row from the first row:
1 - 3/2 2
0 -11/2 -1
Multiply the second row by -2/11:
1 -3/2 2
0 1 2/11
Multiply the second row by 3/2 and add it to the first row:
1 0 25/11
0 1 2/11
Thus x = 25/11 and y = 2/11
Check:
The answer to x2 - 2x - 4y2 - 4y =(x - 2y)(x - 2y - 2)
12y-7
5x - 4y ≥ -203x - 2y ≤ -8y ≥ -3
6(y - 4)
The question contains expressions, not equations. It is not possible to solve linear expressions - whether you use matrices or not.
How do you solve 4y plus x equals 8
Assume the expression is x = 40 - 4y, and assume we want to solve for y. Rearrange the terms to get: x - 40 = -4y y = -¼(x - 40)
4y + 7 = 19 ∴ 4y = 12 ∴ y = 3
So 1. 4x + 3y = 33 2. x = -4y - 25 Two linear equations (degree one polynomial) are likely to be consistent. If you have some knowledge with matrices, using Gaussian Elimination it can be done easily. I will assume that knowledge is not available. It is known that x and y are related in a way such that both equations are satisfied, in particular x = -4y - 25. so 4x is namely 4(-4y - 25) and 4x + 3y = 4(-4y - 25) + 3y which is 33. Simplify the single variable polynomial y and solve for y. It should be an easy way of rearranging things. For the matrix method, post in discussion.
daïras
2
Isolate one of the variable using inverse operations. Then solve. Example: 2x + 4y = 0 --subtract 4y>> 2x = -4y --divide by -4>> -1/2x = y --plug in your variable -->>
Assume the expression is x = 40 - 4y, and assume we want to solve for y. Rearrange the terms to get: x - 40 = -4y y = -¼(x - 40)
The answer to x2 - 2x - 4y2 - 4y =(x - 2y)(x - 2y - 2)
12y-7
Does it say solve for y?
5x - 4y ≥ -203x - 2y ≤ -8y ≥ -3