System of equations : how do I solve it? 3x-y=13 and 2x+2y=10

Answer 1

3x - y = 13

x + y = 5 <--- divides everything by 2

adds them together:

4x = 18

x = 9/2

9/2 + y = 5

9/2 +y = 10/2

y= 1/2

(9/2,1/2)

Answer 2

There are 2 basic methods: Combination and Substitution

Since one equation can easily be solved for y, let's try substitution:

Solve the 1st equation for y:

-y = 13 - 3x

y = 3x - 13

Next, substitute in the second equation (replace y with 3x - 13):

2x + 2( 3x - 13 ) = 10

Expand and simplify:

2x + 6x - 26 = 10

8x = 36

x = 9/2

Finally, plug this into either equation, and solve for y. When you are done, check your answer by putting the values into either equation.