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Use the substitution method to solve the following system of two linear equations.

−14x+15y=0.6
−70x+75y=3
​Write the solution as an ordered pair. For parametric solutions use y=t as the parameter.

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Final answer:

The system of equations −14x+15y=0.6 and −70x+75y=3 are dependent with infinitely many solutions. The general solution using parameter t is (x, y) = (−0.6/14 + 15t/14, t).

Step-by-step explanation:

To solve the system of linear equations −14x+15y=0.6 and −70x+75y=3 using the substitution method, we first observe that the equations are multiples of each other. By simplifying the second equation, we divide each term by 5, yielding −14x+15y=0.6, which is the same as the first equation. This indicates that the equations are dependent, and thus there are infinitely many solutions to this system.

To express the solution, we can use a parameter t for y. For example, set y=t. Substituting t into the first equation gives −14x + 15t = 0.6. Solving for x gives x = −0.6/14 + 15t/14. Thus, the general solution is in the form of an ordered pair (x, y) = (−0.6/14 + 15t/14, t).

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