How do you solve 2x+y=5 and x-y=1?

Question

Eli Assouline · Accepted Answer

#x = 2 " and " y = 1#

In this case we have a perfect scenario because the y terms are additive inverses. When the two equations are added, the y terms will add to 0.

#2x + y = 5 " A"# #x - y = 1 " B"#

A + B: #" " 3x = 6# #" " x = 2#

Substitute #x = 2# in B #2 - y = 1# #2 - 1 = y# #1 = y#

Savannah Anderson · Answer

undefined To solve the system of equations 2x + y = 5 and x - y = 1, you can use the method of substitution or elimination.

Using substitution, solve one of the equations for either x or y, and then substitute that expression into the other equation to solve for the remaining variable. For example, from the second equation x - y = 1, you can solve for x to get x = y + 1. Substitute this expression for x into the first equation:

2(y + 1) + y = 5
2y + 2 + y = 5
3y + 2 = 5
3y = 3
y = 1

Now that you have found y, substitute this value back into the equation x = y + 1 to find x:

x = 1 + 1
x = 2

So, the solution to the system of equations is x = 2 and y = 1.