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Chapter 3: Q19. (page 143)

Solve each system of equations

4a鈭�2b+8c=30a+2b鈭�7c=鈭�122a鈭�b+4c=15

Short Answer

Expert verified

The solution set of the given system of equations is infinitely many solutions.

Step by step solution

01

– Use the elimination method to get the system of equations in two variables.

Multiply the equation 2a-b+4c=15by 2and add the new resultant equation to the equation 4a-2b+8c=30.

Perform the subtraction operation on the new two resultant equations

2a鈭�鈥夆赌�b+4c=154a鈭�2b+8c=30_鈥夆赌夆�夆赌�鈫�multiplyby2鈫�鈥夆赌夆�夆赌夆��鈥夆赌夆�夆赌�4a鈭�2b+8c=30(鈭�)4a鈭�2b+8c=30_鈥夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌夆�夆赌�0=0

02

– Conclude the solutions of the given system of equations. 

Here, 0=0. This means the third equation 2a-b+4c=15is a multiple of first equation 4a-2b+8c=30.

So, they are the same plane.

Hence, the solution of the given system of equations is infinitely many solutions

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Most popular questions from this chapter

Solve each system of equations by graphing.

23x+y=鈭�3y鈭�13x=6

Four lines on a plane intersect in one point, forming 8 equal angles that are non-overlapping. What is the measure, in degrees, of one of these angles ?

Asportinggoodsmanufacturermakesa\(5profitonsoccerballsanda\)4profitonvolleyballs.Cuttingrequires2hourstomake75soccerballsand3hourstomake60volleyballs.Sewingneeds3hourstomake75soccerballsand2hourstomake60volleyballs.Cuttinghas500hoursavailable,andsewinghas450hoursavailable.

What is the maximum profit the company can make from these two products?

Solve each system of equations by graphing.

16.2x+3y=122x鈭�y=4

Using your own words, list the steps in the general

strategy for solving linear equations.
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