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Sagot :
Equation A: x - y = - 3
Equation B: 3x + y = 19
Solve by substitution:
Equation A:
x - y = - 3
x = y - 3
Substitute "y - 3" to "x" in Equation B:
3x + y = 19
3(y - 3) + y = 19
3y - 9 + y = 19
3y + y - 9 = 19
4y = 19 + 9
4y = 28
4y/4 = 28/4
y = 7
Substitute "7" to "y" in Equation A:
x - y = -3
x - 7 = -3
x = -3 + 7
x = 4
x = 4 y = 7
To check:
Equation A:
x - y = -3
4 - 7 = -3
-3 = -3
Equation B:
3x + y = 19
3(4) + 7 = 19
12 + 7 = 19
19 = 19
The system has one solution (4,7)
The lines are intersecting, and the point of intersection is (4,7).
The system has different slopes and y-intercepts.
The system is consistent and independent.
Equation B: 3x + y = 19
Solve by substitution:
Equation A:
x - y = - 3
x = y - 3
Substitute "y - 3" to "x" in Equation B:
3x + y = 19
3(y - 3) + y = 19
3y - 9 + y = 19
3y + y - 9 = 19
4y = 19 + 9
4y = 28
4y/4 = 28/4
y = 7
Substitute "7" to "y" in Equation A:
x - y = -3
x - 7 = -3
x = -3 + 7
x = 4
x = 4 y = 7
To check:
Equation A:
x - y = -3
4 - 7 = -3
-3 = -3
Equation B:
3x + y = 19
3(4) + 7 = 19
12 + 7 = 19
19 = 19
The system has one solution (4,7)
The lines are intersecting, and the point of intersection is (4,7).
The system has different slopes and y-intercepts.
The system is consistent and independent.
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