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Solve the system by substitution. Check your answer.

x+y=2z= - 14
- 3y + z =
7

Z= 4
The solution is
(Type integers or simplified fractions.)

1 Answer

5 votes

The answer is in this explanation below.

To solve the given system of equations by substitution, we'll follow these steps:

1. Start with the first equation: x + y = 2z = -14.

2. Solve the first equation for x in terms of y and z:

x = -14 - y - 2z.

3. Substitute the expression for x into the second equation:

-3y + z = 7.

4. Simplify the equation:

-3y + z = 7.

5. Substitute the given value of z = 4 into the equation:

-3y + 4 = 7.

6. Solve for y:

-3y = 7 - 4,

-3y = 3,

y = -1.

7. Substitute the value of y = -1 back into the first equation to solve for x:

x + (-1) = 2(4) = -14,

x - 1 = 8,

x = 9.

8. Check the solution by substituting the values of x, y, and z into both equations:

For the first equation: 9 + (-1) = 2(4) = -14,

8 = 8, which is true.

For the second equation: -3(-1) + 4 = 7,

3 + 4 = 7, which is also true,

the solution to the system of equations is:

x = 9,

y = -1,

z = 4

Correct me if i'm wrong :>

User LHM
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