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Solve each system of equations by the substitution method.

8x+3y=26

2x=y4

Short Answer

Expert verified

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

Step by step solution

01

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

Add 4 on both the sides of the 2x=y-4and simplify.

2x+4=y4+4

2x+4=y

Substitute 2x+4for y into 8x+3y=26and simplify.

8x+3(2x+4)=26

8x+6x+12=26

14x+12=26

02

Step 2. Solve for one variable.

Subtract 12 from both the sides of the equation obtained in step 2 and simplify.

14x+1212=2612

14x=14

Divide each side of the equation obtained in step 3 by 14 to find the value of x.

14x14=1414

x=1

03

Step 3. Solve for another variable.

Substitute 1 for into 2x=y-4, to find the value of y.

2×1=y4

2=y4

y=6

Therefore, the solution of given system of equations is x = 1, y = 6.

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