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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

3. Linear Functions

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Exercise 4 Page 293

Does either of the equations have an isolated variable in it?

(3,-7)

Practice makes perfect

In this system of equations, at least one of the variables has a coefficient of 1. Therefore, we will approach its solution with the Substitution Method. Observing the given equations, it looks like it will be simplest to isolate x in the first equation using the Properties of Equality.

x+y=-4 & (I) 6x+2y=4 & (II)

(I): LHS-y=RHS-y

x+y-y=-4-y 6x+2y=4

(I): Subtract terms

x=-4-y 6x+2y=4

Now that we've isolated x, we can solve the system by substitution.

x=-4-y 6x+2y=4

(II): x= -4-y

x=-4-y 6( -4-y)+2y=4

▼

Solve for y

(II): Distribute 6

x=-4-y 6(-4)-6(y)+2y=4

(II): a(- b)=- a * b

x=-4-y -6 * 4-6(y)+2y=4

(II): Multiply

x=-4-y -24-6y+2y=4

(II): LHS+24=RHS+24

x=-4-y -24-6y+2y+24=4+24

(II): Add terms

x=-4-y -4y=28

(II): .LHS /(-4).=.RHS /(-4).

x=-4-y -4y/-4=28/-4

MovePartNumRight

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

x=-4-y -4/-4 * y=28/-4

(II): - a/- b=a/b

x=-4-y 4/4 * y=28/-4

(II): a/a=1

x=-4-y 1 * y=28/-4

(II): Identity Property of Multiplication

x=-4-y y=28/-4

MoveNegDenomToFrac

(II): Put minus sign in front of fraction

x=-4-y y=-28/4

(II): Calculate quotient

x=-4-y y=-7

Great! Now, to find the value of x, we need to substitute y=-7 into either one of the equations in the given system. Let's use the first equation.

x=-4-y y=-7

(I): y= -7

x=-4-( -7) y=-7

(I): a-(- b)=a+b

x=-4+7 y=-7

(I): Add terms

x=3 y=-7

The solution, or point of intersection, to this system of equations is the point (3,-7).

Subchapter links

Try It p.290-291

Self-Assessment for Concepts & Skills p.291

Self-Assessment for Problem Solving p.292

Review & Refresh p.293

Concepts, Skills, & Problem Solving p.293-294