Question

What is the solution to the system of equation 2x-y=7 Y=2x+3

Answer 1

4x - y = -4
-y = -4 - 4x (subtract 4x from each side)
y = 4 + 4x (divide by -1)
y = 4x + 4 (commutative property of addition to get the x-value in front). 

Now we must plug what we have gotten y to equal into the other equation. If we try to plug what we have rearranged back into the original equation, we don't get anywhere. 

2x - y = -7
2x - 1(4x + 4) = -7 (substitution)
2x - 4x - 4 = -7 (distributive property with -1)
-2x - 4 = -7 (combine like terms)
-2x = -3 (add 4 to each side)
x = 3/2 (divide by -2). 

You2x-y=7
Y=2x+3 have just solved for x! We can now plug what we have found for x into either equation to get what y equals. (If this is truly a system of linear equations, then it will not matter which one we use.) 

2(3/2) - y = -7 (substitution)

6/2 - y = -7 (multiplication)
3 - y = -7 (division)
- y = -10 (subtraction)
y = 10 (division) 

You have just found y! As a point, the solution to this system is (3/2, 10) with the x-coordinate first and the y-coordinate second. If we plug x and y into both equations, we will find that they will make the equations true. This is how we check ourselves. Using both equations: 

4x - y = -4
4(3/2) - 10 = -4 (does the left half equal -4?)
12/2 - 10 = -4
6 - 10 = -4
-4 = -4 (it does); 

2x - y = -7
2(3/2) - 10 = -7
3 - 10 = -7
-7 = -7.