SOLUTION: Tell whether the ordered pair is a solution of the linear system. (-2,15); y = -3x + 9 y = 5x + 25 Someone please help me with this equation,any help would be appreciated :

Question 128384: Tell whether the ordered pair is a solution of the linear system.
(-2,15);
y = -3x + 9
y = 5x + 25
Someone please help me with this equation,any help would be appreciated :)
Found 2 solutions by checkley71, bucky:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
Y=-3X+9
15=-3*-2+9
15=6+9
15=15 THIS ONE WORKS.
15=5*-2+25
15=-10+25
15=15 THIS ONE ALSO WORKS.
PROOF: (graph 300x300 pixels, x from -6 to 5, y from -10 to 17, of TWO functions -3x +9 and 5x +25).
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
All these two problems involve is taking the x value of the given point and substituting
it in for x in the equation, then taking the y value of the given point and substituting
it for y in the equation, and finally seeing if the equation still balances. If it does, then
you can say the ordered pair of the point is a solution of the linear system.
.
Let's do it. The given point (or ordered pair) has an x value of -2 and a y value of +15.
.
Go to the first equation and substitute -2 for x and + 15 for y. This is done as follows:
.
y = -3x + 9
.
Substitute -2 for x and +15 for y and the equation becomes:
.
+15 = -3(-2) + 9
.
Multiply the -3 times the -2 to get +6 and this makes the equation become:
.
+15 = +6 + 9
.
The sum on the right side is +15 and this makes the equation:
.
+15 = +15
.
Since the equation is balanced (both sides are equal) this tells us that that the ordered
pair (-2, 15) is a solution of the first equation.
.
Now let's go to the second equation you were given:
.
y = 5x + 25
.
Substitute -2 for x and +15 for y and the equation becomes:
.
+15 = 5(-2) + 25
.
Multiply the 5 times the -2 on the right side to get -10 and the equation is then:
.
+15 = -10 + 25
.
The two numbers on the right side combine to give +15 and the equation is then:
.
+15 = +15
.
The equation balances again and this tells you that the ordered pair (-2, +15) is a solution
of the second equation too.
.
Since the ordered pair is a solution of BOTH equations, then it is a solution of the linear set
that contains both equations.
.
Another way you could have done the problem is to solve the pair of equation to see if the
solution of the pair is x = -2 and y = +15. You can do this by substitution or by variable
elimination, or by graphing the two equations and finding the ordered pair where the two
graphs intersect.
.
Let's use substitution.
.
Since the left sides of both equations are both y, the two left sides are equal. And since
the left sides are both equal, then the two right sides also must be equal in the common solution.
In effect we are substituting the value of y from one of the equations (the right side of
that equation) for y in the other equation.
.
When we do that substitution we get:
.
-3x + 9 = 5x + 25
.
Get rid of the 5x on the right side by subtracting 5x from both sides to get:
.
-8x + 9 = 25
.
Next get rid of the +9 by subtracting +9 from both sides to reduce the equation to:
.
-8x = 16
.
Solve for x by dividing both sides of this equation by -8 and you have:
.
x = 16/-8 = -2
.
This tells you that the solution of the set of equations has -2 as its value for x. Knowing
that x = -2 you can now return to either of the two original equations, substitute -2
for x in that equation, and find the value of y. Let's return to the original equation:
.
y = 5x + 25
.
Substitute -2 for x and the equation becomes:
.
y = 5(-2) + 25 = -10 + 25 = +15
.
This tells you the common solution to the two equations is x = -2 and y = +15 which is in
ordered pair form (-2, 15) and this is the point you were asked about. So the ordered pair
(-2, 15) is a solution to the set of equations, just as we found by doing it the other way.
.
Hope this helps you to understand what you were being asked to do and how you would do it.
.
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