Expert: Scott A Wilson - 10/19/2009

Question
how do you solve these problems using the substitution and elimination method,...the problems are 2x+y=13 and 5x-2y=1

Answer
Take the equations 2x+y=13 and 5x-2y=1.

Solve the 1st for y, giving y=13-2x.

Put that in the 2nd, giving 5x-2(13-2x)=1.

Multiply the parenthesis by 2, giving 5x-26+4x=1.

Add 26 to both sides, and combine the x's, giving 9x=27.

Divide both sides by 9, giving x=27/9=3.

Using x=2, take the 1st equation and get 2(3)+y=13.

Multiply by 2, giving 6+y=13.

Subtract 6 from both sides, giving y=7.

Use the 2nd equation to check x=3 and y=7.  This gives 5(3)-2(7)=15-14=1, and that checks.