1.

y=xt1
2x+y=7

2.
x=y-2
3x-y=6

3.
y=2xt3
5x-y=-3

What do want done ?

I can "solve" #2 :

sub the first into the 2nd ...
3(y-2) - y = 6
3y - 6 - y = 6
2y = 12
y = 6
then x = y-2 = 6-2 = 4

for the 1st and 3rd, I have no clue what the
xt1 and 2xt3 are supposed to be.
Is the t a new variable?
is it t^3 ?

To solve these systems of equations, we can use the method of substitution or elimination. I'll explain both methods for each set of equations.

1. Equations:
y = x*t1
2x + y = 7

Method of Substitution:
Step 1: Rearrange the first equation to solve for y:
y = x*t1

Step 2: Substitute the expression for y in the second equation:
2x + x*t1 = 7

Step 3: Simplify and solve for x:
2x + x*t1 = 7
x(2 + t1) = 7
x = 7 / (2 + t1)

Step 4: Substitute the value of x in the first equation to find y:
y = (7 / (2 + t1)) * t1

Method of Elimination:
Step 1: Multiply the first equation by -1 and add it to the second equation to eliminate y:
-1*(y = x*t1) + (2x + y = 7)
-y - 2x - y = -7

Step 2: Simplify the equation:
-2x - 2y = -7

Step 3: Solve the equation:
-2x - 2y = -7
y = (-7 + 2x) / -2

2. Equations:
x = y - 2
3x - y = 6

Method of Substitution:
Step 1: Substitute the expression for x in the second equation:
3(y - 2) - y = 6

Step 2: Simplify and solve for y:
3y - 6 - y = 6
2y = 12
y = 6

Step 3: Substitute the value of y in the first equation to find x:
x = y - 2
x = 6 - 2
x = 4

Method of Elimination:
Step 1: Multiply the first equation by 3 and add it to the second equation to eliminate x:
3*(x = y - 2) + (3x - y = 6)
3x - 6 + 3x - y = 6

Step 2: Simplify the equation:
6x - y - 6 = 6
6x - y = 12

Step 3: Solve the equation:
6x - y = 12
y = 6x - 12

3. Equations:
y = 2x*t3
5x - y = -3

Method of Substitution:
Step 1: Substitute the expression for y in the second equation:
5x - 2x*t3 = -3

Step 2: Simplify and solve for x:
5x - 2x*t3 = -3
x(5 - 2t3) = -3
x = -3 / (5 - 2t3)

Step 3: Substitute the value of x in the first equation to find y:
y = 2 * (-3 / (5 - 2t3)) * t3

Method of Elimination:
Step 1: Multiply the first equation by -1 and add it to the second equation to eliminate y:
-1*(y = 2x*t3) + (5x - y = -3)
-y - 5x + y = 3

Step 2: Simplify the equation:
-5x = 3

Step 3: Solve the equation:
-5x = 3
x = -3/5

Step 4: Substitute the value of x in the first equation to find y:
y = 2 * (-3/5) * t3