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Determine whether the ordered pair is a solution to the system 3x+y=0x+2y=-5

  1. (1,-3)
  2. (0,0)

Short Answer

Expert verified

Part (a) The ordered pair (1,-3)is a solution to the system.

Part (b) The ordered pair (0,0)is not a solution to the system.

Step by step solution

01

Part (a) Step 1. Given Information.

We are given a system of equations,

3x+y=0x+2y=-5

We need to determine whether the point (1,-3)is a solution to the system or not.

02

Part (a) Step 2. Substitute the ordered pair in the first equation.

Substitute 1for xand -3for yin the equation 3x+y=0we get,

3×1+(-3)=03-3=00=0

This is a true statement. So, the point(1,-3)satisfies the first equation.

03

Part (a) Step 3. Substitute the ordered pair in the second equation.

Substitute 1for xand -3for yin the second equation.

x+2y=-5

1+2×(-3)=-51-6=-5-5=-5

This is a true statement, so (1,-3)satisfies the second equation.

As (1,-3)satisfies both the equation so it is a solution of the system3x+y=0x+2y=-5

04

Part (b) Step 1. Given Information.

For the given system3x+y=0x+2y=-5we need to determine whether the point(0,0)is a solution of the system or not.

05

Part (b) Step 2. Substitute the ordered pair in the first equation. 

Substitute 0for xand 0for yin the equation 3x+y=0we get,

localid="1644572937857" 3×0+0=00+0=00=0

As the statement is true so the point(0,0)satisfies the first equation.

06

Part (b) Step 3. Substitute the ordered pair in the second equation. 

Substitute 0for xand 0for yin the equation x+2y=-5we get,

localid="1644572948618" 0+2×0=-50+0=-50=-5

As the statement is false, so (0,0)does not satisfy the second equation.

07

Part (b) Step 4. Conclusion.

Thus, the point0,0is not the solution of the system.

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