What is the solution of x + y = 2 and 2x + 5y = 16?

a.) x=1, y=4

b.)x=4, y=-2

c.)x=-2, y=-2

d.)x=-2, y=4

HELP!!!!!!

Question

What is the solution of x + y = 2 and 2x + 5y = 16?

a.) x=1, y=4

b.)x=4, y=-2

c.)x=-2, y=-2

d.)x=-2, y=4

HELP!!!!!!

imstuck · Answer

To do this, you can either use substitution or the addition method.  Here it will probably be easier to use substitution.  Look at the first equation:  x + y = 2.  If you solve this equation for y, you now know y's value in terms of x.  y = 2 - x.  Now that you "know" what y is, substitute it into your second equation.$$y=2-x-->2x+5(2-x)=16$$Now you have an equation that only has one variable in it instead of 2.  Distribute the 5 into your (2 - x) to get 10 - 5x.  Now your equation looks like this:$$2x+10-5x=16$$Now, do the math!  2x - 5x = -3x.  -3x + 10 = 16.  Subtract the 10 from both sides and you have -3x = 6, and solving for x gives you -2.  NOW you know x and you can find y.  Substitute -2 in for x in either of your equations (I would pick the first one because it's simpler to solve).  x + y = 2 yields -2 + y = 2.  Now solve for y.  Add 2 to both sides and y = 4.  See that?