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How do you solve linear combination 5x equals 4y-30 and 2x plus 3y equals -12?
Wiki User
∙ 11y ago
Here is one possible method of solving the system: 5x = 4y - 30
2x + 3y = -12
Rewrite to line up variables:
5x - 4y = -30
2x + 3y = -12
Multiply the top equation by 2 and the bottom equation by 5:
10x - 8y = -60
10x + 15y = -60
Subtract the two equations:
-23y = 0;
So y = 0; plug back into an original equation to find x:
2x + 3(0) = -12
2x = -12
x = -6The solution to the system is x = -6 and y = 0, or the point (-6,0).
Wiki User
∙ 11y ago
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Is the system 3x 2y15 6x 4y30 consistent?
Set up an augmented matrix and use Gaussian elimination to solve the system: 3 2 | 15 6 4 | 30 ~2 * R1 -> R1 6 4 | 30 6 4 | 30 ~ -1 * R1 + R2-> R2 6 4 | 30 0 0 | 0 ~ 1/6 * R1 -> R1 1 2/3 | 5 0 0 | 0 We can conclude two things from this: 1) The system is consistent, because there are no "bad" rows (no row reduces down to 0 ... | 1) 2) There is a free variable. The solution to the system is x + 2/3y = 5, where 'y' is free.
