Problem

3x−y+z+7w=13−2x+y−z−3w=−9−2x+y−7w=−8

Answer

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Answer

7. Substitute 'z', 'w', and 'x' into Eq. (2) to find 'y': \ −2⋅4+y−837−3⋅937=−9⇒y=−2

Steps

Step 1 ：1. Eliminate 'y' by adding Eq. (1) and Eq. (2): \ x+4w=4

Step 2 ：2. Eliminate 'y' by adding Eq. (1) and Eq. (3): \ x+7z+14w=5

Step 3 ：3. Combine Eq. (4) and Eq. (5) to eliminate 'x' and solve for 'z': \ 3z+10w=1⇒z=1−10w3

Step 4 ：4. Substitute 'z' from Eq. (6) into Eq. (4) and solve for 'w': \ x+131−10w3=4⇒w=937

Step 5 ：5. Substitute 'w' into Eq. (6) to find 'z': \ z=1−10⋅9373=837

Step 6 ：6. Substitute 'z' and 'w' into Eq. (1) to find 'x': \ 3x−837+937+7⋅937=13⇒x=4

Step 7 ：7. Substitute 'z', 'w', and 'x' into Eq. (2) to find 'y': \ −2⋅4+y−837−3⋅937=−9⇒y=−2

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