Exercise 3 Page 209

We can determine the number of solutions to the system by graphing the given equations. This will be the point at which the lines intersect. To do this, we will need the equations to be in slope-intercept form to help us identify the slope m and y-intercept b.

Writing in Slope-Intercept Form

Let's rewrite each of the equations in the system in slope-intercept form, highlighting the m and b values.

Graphing the System

We will start by plotting the y-intercepts to graph these equations. Then, we will use the slope to determine another point that satisfies each equation, and connect the points with a line.

We can see that the lines intersect at exactly one point.

The point of intersection at (3,- 5) is the one solution to the system.

Showing Our Work

Showing Our Work

In case you want to see the steps we took to rewrite the equations in slope-intercept form, we have included these calculations.

4x+2y=2 & (I) 3x=4-y & (II)

SubEqn

(I): LHS-4x=RHS-4x

2y=2-4x 3x=4-y

DivEqn

(I): .LHS /2.=.RHS /2.

2y2= 2-4x2 3x=4-y

▼

(I): Simplify

MovePartNumRight

(I): a* b/c=a/c* b

22y= 2-4x2 3x=4-y

QuotOne

(I): a/a=1

1y= 2-4x2 3x=4-y

IdPropMult

(I): Identity Property of Multiplication

y= 2-4x2 3x=4-y

FactorOut

(I): Factor out 2

y= 2(1-2x)2 3x=4-y

CancelCommonFac

(I): Cancel out common factors

y= 2(1-2x)2 3x=4-y

SimpQuot

(I): Simplify quotient

y= 1-2x1 3x=4-y

DivByOne

(I): a/1=a

y=1-2x 3x=4-y

CommutativePropAdd

Commutative Property of Addition

y=- 2x+1 3x=4-y

AddEqn

(II): LHS+y=RHS+y

y=- 2x+1 3x+y=4

SubEqn

(II): LHS-3x=RHS-3x

y=- 2x+1 y=4-3x

CommutativePropAdd

(II): Commutative Property of Addition

y=- 2x+1 y=- 3x+4