Solving Systems of Linear Equations by Graphing
Solve the system of linear equations by graphing:
y = 2x + 9
y = -x + 6
(-1,7)
Solve the system of linear equations by substitution:
y = x - 4
y = 4x - 10
(2,-2)
Solve the system of linear equations by elimination:
x + 3y = 5
-x - y = -3
(2,1)
Solve the equation:
5(2 - y) + y = -6
y = 4
Solve the system of linear equations:
y = 3x - 8
y = 3x - 8
Infinite solutions
Solve the system of linear equations by graphing:
y = x + 4
y = -x + 2
(-1,3)
Solve the system of linear equations by substitution:
y = 2x + 5
y = 3x - 1
(6,17)
Solve the system of linear equations by elimination:
x - 2y = -7
3x + 2y = 3
(-1,3)
In y=mx+b what does the m and the b represent?
m is the slope and b is the y-intercept
Solve the system of linear equations:
y = 3x + 1
-x + 2y = -3
(-1,-2)
Solve the system of linear equations by graphing:
y = 2x + 5
y = 0.5x - 1
(-4,-3)
Solve the systems of equation by substitution
y = 6
–x + y = 2
(4, 6)
Solve the system of linear equations by elimination:
2x + 7y = 1
2x - 4y = 12
(4,-1)
Decide whether the two equations are equivalent and solve if possible.
4n + 1 = n - 8
3n = -9
Yes; n = -3
Solve the system of linear equations:
y = 5x - 9
y = 5x + 9
No solution.
Solve the system of linear equations by graphing:
x + y = 7
y = x + 3
(2,5)
Solve the system of linear equations by substitution:
2x = y - 10
x + 7 = y
(-3,4)
Solve the system of linear equations by elimination:
2x - y = 0
3x - 2y = -3
(3,6)
Solve the system of linear equations by substitution
y=2x-5
-x+y=2
(7,9)
Solve the system of linear equations:
y = 8x - 2
y - 8x = -2
Infinitely many solutions.
Is it possible for a system of linear equations to have exactly two solutions? Explain your reasoning.
No, two lines cannot intersect in exactly two points.
Solve the system of linear equations by substitution:
y - x = 0
2x - 5y = 9
(-3,-3)
Solve the system of linear equations by elimination:
x + 4y = 1
3x + 5y = 10
(5,-1)
Is (1,1) a solution to the system of equations?
2x+y=3
3x−y=7
No
2(1) + (1) = 3
3 = 3 CORRECT
3(1) - (1) = 7
4 = 7 WRONG
Describe and correct the error in solving the system of linear equations.
y = -2x + 4
y = -2x + 6
The lines have the same slope so there are infinitely many solutions.
The lines have the same slope but different y-intercepts so therefore they are never going to intersect = No Solution.
Solve the system of equations using the substitution method:
3x - y= 7
y = 2x - 4
(3, 2)