4z + 3 = 6 + 2z
Subtract 2z from each side of the equation:
2z + 3 = 6
Subtract 3 from each side:
2z = 3
Divide each side by 2:
z = 3/2 = 1.5
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I used the matrix method to find the answer: x=4, y=-7, z=-5.
To solve for h, first isolate 4h: T=4h+4z T-4z=4h Now divide both sides by 4. T/4-z=h
9z
7 + 4z = 437 + 4z -7 = 43 - 7 4z = 43 - 7 4z = 36 z = 9
4x + 3y + 2z = 34; 2x + 4y + 3z = 45; 3x + 2y + 4z = 47 First, eliminate terms in z from 2 of the equations, by muliplying first equation by 2 and subtracting third equation from the answer: 8x + 6y + 4z = 68, subtract leaving 5x + 4y = 21 (equation 4) Similarly multiply the first equation by 3 and the second by 2 giving 12x + 9y + 6z = 102 and 4x + 8y + 6z = 90 Subtract again and we have 8x + y = 12 or y = 12 - 8x Substitute this in equation 4 gives 5x + 4(12 -8x) = 21 Simplify: 5x + 48 - 32x = 21 = -27x = -27 so x = 1 y = 12 - 8x so y = 4 and in one of the original equations 4 + 12 + 2z = 34, ie 2z = 34 -16 so z =9 Check: 2x + 4y + 3z = 2 +16 + 27 = 45 and 3x + 2y + 4z = 3 + 8 + 36 = 47 QED!