For each order pair determine whether it is a solution to the system of equations
y=2x+1
-5x+3y=8
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(x,y) (3, -2) it is a solution yes or no
(-7,-9) it is a solution yes or no
(5,11) it is a solution yes or no
(0,1) it is a solution yes or no
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Solving by substitution
y=2x+1 (I)
-5x+3y=8 (II)
Replacing (I) in (II)
-5x+3 (2x+1 ) =8
-5x + 6x + 3 = 8
(-5 +6) x = 8-3
x=5
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y=2x+1
y = 2*5 + 1
y= 11
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Answer
(5,11) it is the solution
A system of two linear equations has only one ordered pair that solves it
Graphically it is the interception of the lines
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Verifying
(3, -2) it is a solution yes or no
y=2x+1
-2=2*3+1
-2= 7
It is not possible
-2≠ 7
The ordered pair (3, -2) is not a solution
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Verifying
(-7,-9) it is a solution yes or no
y = 2x+1
9 = 2*-7 +1
9 = -14+1
It is not possible
9 ≠ -15
The ordered pair (-7,-9) is not a solution
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Verifying
(0,1) it is a solution yes or no
y = 2x+1
1 = 2*0 + 1
It is possible
-5x+3y=8
-5*0+3*1 = 8
3 = 8
3 ≠ 8
The ordered pair (0, 1) is not a solution
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There is just one possible solution and it is (5,11)
y = 2x+1
11 = 2*5 +1
11 = 11
It is possible
-5x+3y = 8
-5*5 +3* 11 = 8
-25 +33 = 8
8 = 8
It is possible
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Answer
The ordered pair (3, -2) is not a solution
The ordered pair (-7,-9) is not a solution
The ordered pair (0,1) is not a solution
There is just one possible solution and it is (5,11)