Solve the system using the elimination method.
Solve the system using the elimination method. -8x - 4y + 2z = -26 -2x + 4y + 2z = 10 -6x - 8y - 5z = -41
It appears that the three equations are:
1) -8x - 4y + 2z = -26
2) -2x + 4y + 2z = 10
3) -6x - 8y - 5z = -41
Subtract equation two from equation one, eliminating the z.
-8x - 4y + 2z = -26
-(-2x + 4y + 2z = 10)
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-6x - 8y = -36
4) -6x - 8y = -36
Multiply equation two by 5.
5 * (-2x + 4y + 2z) = 10 * 5
5) -10x + 20y + 10z = 50
Multiply equation three by 2.
2 * (-6x - 8y - 5z) = -41 * 2
6) -12x - 16y - 10z = -82
Add equation six to equation five, again eliminating the z.
-10x + 20y + 10z = 50
+(-12x - 16y - 10z = -82)
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-22x + 4y = -32
7) -22x + 4y = -32
Multiply equation seven by 2.
2 * (-22x + 4y) = -32 * 2
8) -44x + 8y = -64
Add equation eight to equation four, eliminating the y.
-6x - 8y = -36
+(-44x + 8y = -64)
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-50x = -100
-50x = -100
x = 2 <<<<<<<<<<<<<<<<<<<<
Substitute the value of x into equation four.
-6x - 8y = -36
-6(2) - 8y = -36
-12 - 8y = -36
-8y = -36 + 12
-8y = -24
y = 3 <<<<<<<<<<<<<<<<<<<<
Substitute both x and y into equation one.
-8x - 4y + 2z = -26
-8(2) - 4(3) + 2z = -26
-16 - 12 + 2z = -26
-28 + 2z = -26
2z = -26 + 28
2z = 2
z = 1 <<<<<<<<<<<<<<<<<<<<
Substitute all three values into equation two.
-2x + 4y + 2z = 10
-2(2) + 4(3) + 2(1) = 10
-4 + 12 + 2 = 10
-4 + 14 = 10
10 = 10
Substitute all three values into equation three.
-6x - 8y - 5z = -41
-6(2) - 8(3) - 5(1) = -41
-12 - 24 - 5 = -41
-36 - 5 = -41
-41 = -41
Everything checks.
x = 2, y = 3, z = 1