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Chapter 3: Q4. (page 142)

Solve each system of equations.

4.

x+2y=123y鈭�4z=25x+6y+z=20

Short Answer

Expert verified

The solution is x=6,y=3,z=-4.

Step by step solution

01

Step-1 –Using elimination to obtain two equations in two variables

Given equations are

x+2y=123y鈭�4z=25x+6y+z=20

Subtracting the third equation from the first equation, we get

2y鈭�6y鈭�z=12鈭�20鈭�4y鈭�z=鈭�84y+z=鈭�8

02

Step-2 –Solving the system of two equations in two variables

System of equations in two variables are

3y+16y=25+3219y=57y=3

Substituting the value ofyin first equation, we get

3y鈭�4z=253(3)鈭�4z=25鈭�4z=25鈭�9鈭�4z=16z=鈭�4

03

Step-3 –Putting the value of y and z in any of the equation with all three variables

x+6y+z=20x+6(3)鈭�4=20x+18鈭�4=20x=20鈭�14x=6.

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Most popular questions from this chapter

58b+12=-34

Solve each system of equations by graphing.

y=3x鈭�8y=x鈭�8

14(p-7)=13(p+5)

Graph each system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum values of the given function.

15. How many soccer balls and volleyballs should be made to maximize the profit?

13(x+5)=56
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