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Chapter 4: Q. 70 (page 387)

Solve the system of equations by elimination and explain all your steps in words:

5x+4y=102x=3y+27

Short Answer

Expert verified

The solution of system of system of linear equation 5x+4y=102x=3y+27is (6,-5)

Step by step solution

01

Given information and creating variable with same coefficient

Given equations:

5x+4y=10鈥�..(1)2x=3y+27鈥�..(2)

Both equations are in standard form. So, elimination will work.

Multiply the first equation with 3.

3(5x+4y)=3(10)

Simplify parenthesis:

localid="1658851619517" 15x+12y=30.....(3)

Multiply the second equation with 4

localid="1658851625849" 4(2x)=4(3y+27)8x=12y+1088x-12y=108....(4)

02

solving for x and y

Solving equation 3and 4

Adding equations 3 and 4 we get

x=138梅23

x=6

Substitute x=6in any one of the equations and solve for localid="1658851682925" y

Consider:5x+4y=10

Substitute:

5(6)+4y=10

Multiply:

30+4y=10

4y=-20

y=-20梅4

y=-5

Hence the solution is(6,-5)

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