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Systems of Equations
Solve a system of equations by 1. graphing
2. substitution
3. elimination
You are looking for the point of intersection.
Graphing
Graph the lines and find the intersection point
Substitution
Solve one equation for a variable and substitute it in the other equation.
Elimination Line up the 2 equations, add or subtract to get rid of a variable.
1. Solve each pair of equations by substitution.
a. x + 4y = -1
b. y = 10x + 212
y = 3x – 10
x + y = 245
c. y = -5x + 37
20x + 13y = -734
d. 10x – 3y = -490
y = 100 – 3x
e. y = 0.3x + 21.5
x + 2y = 123
f. y = -0.25x + 200
3x – 4y = -160
g. 9x + 6y = -42
y = -5x
h. y = -3x + 12
5x + 4y = 27
i. 2x + 3y = -10
y = -6x + 18
j. 4x – 5y = -17
y = 3x + 10
2. Find the solution common to each pair of equations by substitution.
7
a. y = -6x – 3
b. y = x + 5
c. 2x + 4y = 20
5
1
3x + 5y = 28
y = 5x + 19
y = x + 11
5
3. Find the solution common to each pair of equations, using the method of elimination.
a. 3x + 4y = 5
b. 6x – 7y = 4
c. 6x + 2y = 6
5x – 4y = -13
5x – 2y = 11
9x + 2y = 9
d. 8x + 6y = -2
9x + 3y = -6
e. 3x – 2y = 15
9x + 4y = 75
g. 2x + 4y = 5
3x + 4y = 7
h. 4x – 2y = 6
8x + 2y = 10
f. 6x + 3y = -21
5x + 5y = -25