SOLUTION: For each ordered pair, determine whether it is a solution to the system of equations:? For each ordered pair, determine whether it is a solution to the system of equations: y

Question 844906: For each ordered pair, determine whether it is a solution to the system of equations:?
For each ordered pair, determine whether it is a solution to the system of equations:
y=-2x-5
6x+3y=-15
(5,0),(2,7),(4,-13),(-3,1)
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Solve the given system and pick the point that matches the solution.

Substitute the formula for y into the second standard form equation and find the x value, and use the formula for y, the first equation, using that found value of x.

6x+3y=-15 ------Given
6x+3(-2x-5)=-15
6x-6x-15=-15
0-15=-15 obviously true; so then what must be x?

Try solving the second equation for y in terms of x.
3y=-6x-15
y=-6x/3-15/3
y=-2x-5, which is the same as the first equation, that same formula for y.
The two equations are equivalent!

TEST EACH x COORDINATE and find if the y value matches the coordinate for y found in the point.
x=5, y=-2(5)-5=-15. No match.
x=2, y=-2*2-5=-9. No match.
x=4, y=-2*4-5=-13. MATCH.
x=-3, y=-2(-3)-5=1. MATCH.
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CONCLUSION: The points on the two equivalent lines are (4,13) and (-3,1).
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