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Chapter 2: Q8. (page 69)

Solve each system of equations by the substitution method.

x鈥�7y=13

3x鈥�5y=23

Short Answer

Expert verified

The solution of given system of equations is x = 6, y = 鈥� 1.

Step by step solution

01

Step 1. Substitute value of one variable from one equation to another.

Add 7y on both the sides of x-7y=13and simplify.

x鈭�7y+7y=13+7y

x=13+7y

Substitute 13+7yfor into 3x-5y=23and simplify.

313+7y鈭�5y=23

39+21y鈭�5y=23

39+16y=23

16y=鈭�16

02

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 2 by 16 to find the value of y.

16y16=鈭�1616

y=鈭�1

03

Step 3. Solve for another variable.

Substitute -1for into x-7y=13, to find the value of x.

x鈭�7鈭�1=13

x+7=13

x=6

Therefore, the solution of given system of equations isx = 6, y = 鈥� 1.

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