Answer:
b) y = 3x + 1
y = x+1
Explanation:
Select all the systems of equations that have exactly one solution.
a)
y = 3x + 1
y = 3x + 7
y - 3x = 1.... Equation 1
y - 3x = 7...... Equation 2
We solve using Elimination
We Subtract Equation 2 from 1
(y - y ) - (3x - 3x) = 7 - 1
0 = 6
b) y = 3x + 1...... Equation 1
y = x +1...... Equation 2
x = y - 1
We substitute y - 1 for x in Equation 1
y= 3(y - 1) + 1
y = 3y - 3 + 1
y - 3y = -3 + 1
-2y = -2
y = -2/-2
y = 1
Solving for x
x = y - 1
x = 1 - 1
x = 0
x = 0, y = 1,
The Equations in b) have only one solution
c) x+y=10
x = 10 - y
2x+2y=20
We substitute
2(10 - y) + 2y = 20
20 - 2y + 2y= 20
-2y + 2y = 20 - 20
0 = 0
It has no solution
d) x+y=10.... Equation 1
x+y=12..... Equation 2
We solve using Elimination
We Subtract Equation 2 from 1
x - x + y - y = 12 - 10
0 = 2