Page 428 - Algebra 1

Example
2
Subtracting Equations
Solve the system by elimination. 7x + 3y = -5 2x + 3y = 5
SOLUTION
Hint
Subtracting is the same as adding the opposite.
7x + 3y = -5 2x+3y= 5
Both equations have the same positive coefficient for one of the variables.
Subtract the equations and combine like terms. Divide both sides by 5.
____ __ 5x = -10
x = -2
Substitute -2 for x in one of the original equations and solve for y.
2x + 3y = 5 2(-2)+3y=5 -4 + 3y = 5 3y = 9 y=3
Substitute -2 for x in the second equation. Multiply.
Add 4 to both sides. Divide both sides by 3.
The solution is (-2, 3).
Sometimes it may be necessary to first multiply one or both of the equations
by a number in order to have opposite coefficients.
Multiplying One Equation
Solve the system by elimination. 5y = 8x - 2 4x - 3y = -2
Example
3
SOLUTION
Hint
Make sure both equations are in standard form in order to easily combine like terms.
-8x + 5y = -2 8x - 6y = -4
Write the first equation in standard form. Multiply the second equation by 2.
Add the equations and combine like terms. Simplify.
____ __ -y = -6
y = 6
Substitute 6 for y in one of the original equations and solve for x.
5y = 8x - 2 5(6) = 8x - 2 30 = 8x - 2
32 = 8x 4 = x
Substitute 6 for y in the first equation. Multiply.
Add 2 to both sides.
Divide both sides by 8.
The solution is (4, 6).
Lesson 63 413