Aim: How do we solve systems of equations algebraically?

Do Now: Solve the system of linear equations

x – 2y = 4

y = 3 – 2x

HW: p.237 # 20,22,24,28,30,34, # 38- 43

(2,-1)

Solve the system: y = 2x +1

y = x2 + 4x + 1

Replace y in 2nd equation by 2x + 1

2x + 1 = x2 + 4x + 1

Move all the terms to one side of the equation x2 + 2x = 0

Solve for x x (x + 2) = 0 x = 0, x = – 2

Substitute 0 and – 2 in 1st equation

y = 2(0) + 1 = 1 y = 2(-2) + 1 = – 3 (0,1) (-2,-3)

(0,1) (-2,-3)

Solve the system: x2 + 4y2 = 4 x = 2y – 2

Replace x in 1st equation by 2y – 2

(2y – 2)2 + 4y2 = 4

Multiply and simplify the equation

(2y – 2)(2y – 2) + 4y2 = 4 4y2 – 8y + 4 + 4y2 = 4

8y2 – 8y = 0

Solve for y 8y(y – 1) = 0, y = 0, y = 1

Replace y into 2nd equation x = 2(0) – 2 = - 2

x = 2(1) – 2 = 0(-2,0)(0,1)(-2,0) (0,1)

Solve the system algebraically: y = x2 – 4

y = – 2x

42 2 xx Replace y in 1st equation by – 2x

0422 xx The equation is not factorable, then use the formula

2

1642 x

2

202

2

522 51

Replace x into the 2nd equation to find y

522)51(2,51 yx522)51(2,51 yx

)522,51( and )522,51(

2

1022

xy

yx

Let’s identify and graph each of these equations. What do they look like?

A circle centered at (0, 0) with radius square root of 10

A line with slope 1 and y int. 2

From the second equation we know what y equals so let’s sub it in the first equation.

102 22 xx

104422 xxxFOIL this

2

1022

xy

yx 104422 xxx0642 2 xx

0322 2 xx

0132 xx

1,3 xx1y 3y (-3, -1)

(1, 3)

1. Solve the system: y = x2 – 8x + 15

y = – x + 5

2. Solve the system: xy = – 6

x + 3y = 3

3. Solve the system: x2 – 2y2 = 11

y = x + 1

(2,3) (5,0)

(-2,3) (6,-1)

)31,32)(31,32( iiii