Name: _________________________________
Algebra 1 300 – Unit 4 Test Review
Date: __________________________________
We have examined three different methods to solving Systems of Equations.
Method
1. Graphing Method
Steps
1) Write equations in slope-intercept form.
2) Graph each line using the y-intercept and slope.
3) Find the intersecting point.
4) Check the point of intersection.
2. Substitution Method
1) Transform (rewrite) one of the two equations (“x =” or “y =”).
2) Substitute that transformed equation into the untouched equation.
3) Solve for the variable.
4) Use that answer to find the other variable by plugging it in to either of
the original equations.
5) Write the answer as an ordered pair (x, y).
6) Check the solution.
3. Elimination Method
1) (if needed) Multiply one/both of the equations so that you have a
“matched” coefficient for one of the variables.
2) Add/Subtract the equations in order to Eliminate one of the variables.
(It all depends on the coefficients and signs of each variable.)
3) Solve the resulting equation for the variable.
4) Use that answer to find the other variable by plugging it back into one
of the original equations.
5) Check your answers.
6) Write the answer as an ordered pair (x, y).
3 Possible Solutions to
Systems of Equations
1) Intersecting Lines: You are able to find an (x , y) SOLUTION.
2) Parallel Lines: Variables go away and you are left with a FALSE
statement. NO SOLUTION
3) Coinciding (same) Lines: Variables go away and you are left
with a TRUE statement. INFINITELY MANY SOLUTIONS.
Solve each system by the Graphing Method.
1)
3)
y  x  2
y  2x  5
y  2 x  5
y  x  3
1
x 1
2)
2
4 x  8 y  8
y
4)
2y  x  2
x  2y  8
Solve each system by the Substitution Method.
5)
7)
y  x2
6)
2 x  y  17
y  3x  7
8)
6 x  2 y  12
3 y  x  9
2 y  5 x  11
3x  1  y
2 x  3 y  25
Solve each system by the Elimination Method.
9)
12 x  3 y  18
5x  3 y  4
10)
2 x  7 y  41
6 x  5 y  7
1
1
x  y  4
2
3
11)
1
1
x  y  2
5
5
12)
3 x  2 y  16
5x  2 y  8
Solve using any method you choose.
13) There are 812 students in a school. There are 36 more girls than boys. How many girls are there?
14) The length of a rectangle is 5 more than twice the width. The perimeter is 130. What is the area?
15) Rebecca has 45 coins, all nickels and dimes. The total value of the coins is $3.60. How many of
each coin does she have?
Cumulative Review
Write the inequality from the given graph.
16.)
17.)
Tell whether the value given is a solution to the inequality.
18.)
19.)
Solve the inequality. Graph the solution.
20.) 3x  7 x  2  10  12
21.) 5 – x + 6(x – 2) > 5(x + 1)
Solutions
1) (-1, 3)
2) INFINITE SOLUTIONS
3) (2, -1)
4) NO SOLUTION
5) (5, 7)
6) (3, -2)
7) NO SOLUTION
8) (2, 7)
9) (2, -2)
10) (3, -5)
11) (-4, -6)
12) (3, -7/2)
13) 424 girls
14) Area = 900 square units
15) 18 nickels, 27 dimes
16) x < 8
17) x > -5
18) Yes
19) Yes
20) x > 1
21) No Solution