Question

1.y = 6xSolve:(4x + y = 72.y = 3xsolve: { x + 2y + 703Which equation, together with y = -1.5x + 3, makes a system with one solution?Ay = -1.5x + 6B.y = -1.5xC.2y = -3x + 6D.2y + 3x = 6IE.y = -2x + 34.The system x - 6y = 4, 3x - 18y = 4 has no solution.a.Change one constant or coefficient to make a new system with one solution.b.Change one constant or coefficient to make a new system with an infinite number ofsolutions5.Match each graph to its equation.Im

Answer 1

The system of equations:

`\begin{gathered} x-6y=4 \\ 3x-18y=4 \end{gathered}`

This comes from the fact that if we multiply the first equation by 3 then we have:

`3x-18y=12`

But this clearly contradicts the second one. Then the system has no solutions.

a.

To find a system with one solution we only have to change one of the coefficients of the equation. If we change the first x coefficient from 1 to 2. then we have the system:

`\begin{gathered} 2x-6y=4 \\ 3x-18y=4 \end{gathered}`

which has one solution.

b.

To find a system with an infinite number of solutions we can change the constant of the second equation to 12, then:

`\begin{gathered} x-6y=4 \\ 3x-18y=12 \end{gathered}`

then if we multiply the first by 3 then we have the second one, therefore the equations are the same and the system will have and infinite number os solutions.