Is (-8, 5) a solution to the system of equations: y = 10x + 6, y = 5x + 4?

Understand the Problem

The question asks whether the point (-8, 5) satisfies the system of equations provided. To solve it, you need to substitute x = -8 and y = 5 into both equations and check if both equations hold true. If both equations are true, then (-8, 5) is a solution.

Answer

No, because $5 \neq 10(-8) + 6$ and $5 \neq 5(-8) + 4$.

Steps to Solve

Substitute $x = -8$ and $y = 5$ into the first equation

Plug in the values into the first equation $y = 10x + 6$: $5 = 10(-8) + 6$

Simplify the first equation

Now simplify the right side of the equation: $5 = -80 + 6$ $5 = -74$ Since $5 \neq -74$, the first equation is not satisfied.

Substitute $x = -8$ and $y = 5$ into the second equation

Plug in the values into the second equation $y = 5x + 4$: $5 = 5(-8) + 4$

Simplify the second equation

Now simplify the right side of the equation: $5 = -40 + 4$ $5 = -36$ Since $5 \neq -36$, the second equation is not satisfied.

Determine if (-8, 5) is a solution

Since the point (-8, 5) does not satisfy either equation, it is not a solution to the system of equations.

More Information

A solution to a system of equations must satisfy all equations in the system. In this case, the point (-8, 5) did not satisfy either equation.

Tips

A common mistake is to only test the point in one of the equations. To be a solution to the system of equations, the point MUST satisfy ALL equations.

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