Name: ______Date: ______Hour: ______

LINEAR SYSTEMSSolving systems of linear equations.

x + y = 13
x – y = 7 / x + 3y = 10
3x – 2y = -14
Easy / Difficult

1.Find the solution to the “Easy” system of equations above. Show your work and circle your final answer.

2.There is a solution to the “difficult” system of equations. But it is not easy to find. Follow these steps.

a. Fill in the table with 3 possible solutions to the first equation:
X + 3y = 10
X | Y .
b. Graph your solutions to the first equation. Connect the points.
c. Fill in the table with 3 possible solutions to the second equation:
3X – 2y = -14
X | Y .
D. Graph your solutions to the second equation on the same graph. Connect the points.
e. Where do the two graphs meet?
X = ______y = ______
f. Plug the x and y value for part E into both “hard” equations. Do they fit both? Show your work. /

3.Find a solution to each of the following system of equations by making a table and graphing or adding the equations together. One of the pairs doesn’t have a solution. Explain why.

A. x + y = -4
-x + y = 2
C. – 2x + y = 4
4x – y = -2
E. 2x + y = 2
Y = -2x + 6 / B. x + y = -2
0X + y = -6
D. x – y = 6
2x + y = 0
F. 4x + 2y = 6
2x = -y + 3

Extra graph paper: (as needed)

4. Find a solution to each of the following system of equations by adding the equations together. The last one needs to be multiplied by something before adding.

A. x + y = 3
x – y = 5
C. x – y = 5
2x + y = 1
E. 5x + 3y = 10
3Y = 2x – 4 / B. -x + y = -6
X + y = 2
D. -2x + 3y = 8
2x + y = 0
F. x + y = 4
3x – 2y = 7

5.Put each of the following equations into slope-intercept form (y = mx + b) and state their slope and y-intercept. Graph them and find the point where the graphs intersect. Substitute the values into both equations to verify the intersection is a solution.

a. x + y = 3 x – y = 1
-x -x
y = -x + 3
(slope-intercept form)
Slope = -1 . Slope = .
Intercept= 3 . Intercept= .
Point of Intersection (____, ____) /
B. x = -y x + y = 4
Slope = . Slope = .
Intercept= . Intercept= .
Point of Intersection (____, ____) /
C. -3x = 5 – y 2y = 6x + 10
Slope = . Slope = .
Intercept= . Intercept= .
Point of Intersection (____, ____) /
D. x = ½ y + 1 x – 2y = -2
Slope = . Slope = .
Intercept= . Intercept= .
Point of Intersection (____, ____) /