Two systems of equations are shown below: System A System B 2x + y = 5 −10x + 19y = −1 −4x + 6y = −2 −4x + 6y = −2 Which of the following statements is correct about the two systems of equations? They will have the same solutions because the first equation of System B is obtained by adding the first equation of System A to 2 times the second equation of System A. They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A. The value of x for System B will be −5 times the value of x for System A because the coefficient of x in the first equation of System B is −5 times the coefficient of x in the first equation of System A. The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −12 to the first equation of System A and the second equations are identical.

"They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A."

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MrRoyal MrRoyal · Answer 2 · 2021-11-05T15:27:38+01:00

The solution to the system of equations is the true value of the equations.

The true statement is: (a) They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 3 times the second equation of System A.

The systems of equations are:

[tex]\mathbf{2x + y = 5}[/tex] and [tex]\mathbf{-4x + 6y = -2}[/tex]

[tex]\mathbf{-10x + 19y = -1}[/tex] and [tex]\mathbf{-4x + 6y = -2}[/tex]

The first system is given as:

[tex]\mathbf{2x + y = 5}[/tex] and [tex]\mathbf{-4x + 6y = -2}[/tex]

Equation (1) is transformed as follows:

[tex]\mathbf{2x + y = 5 + 3(-4x + 6y = -2)}[/tex]

[tex]\mathbf{2x + y = 5 + (-12x + 18y = -6)}[/tex]

Collect like terms

[tex]\mathbf{2x -12x+ y+18y = 5 -6}[/tex]

[tex]\mathbf{10x+ 19y = -1}[/tex]

Notice that:

[tex]\mathbf{10x+ 19y = -1}[/tex] is the first equation of the second system.

This means that, the two systems of equation would have the same solution.

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