Create a system of linear equations that has one solution. Solve the system using substitution to prove your
that your system has only one solution.

So the best way to solve is to come up with two slopes, I'd prefer 2 perpendicular slopes because perpendicular lines only cross once hence one solution guaranteed
so say we choose a slopeA = 2 and slopeB = -1/2, the slopes are perpendicular only if when you multiply them you get -1
then we use the slope intercept form of an equation y = mx + b
we make up two equations y = -2x + b and y = -1/2x + b , now we can just make up number for b so the two equations are
y = -2x + 3
y = -1/2x + 5
Then we solve them by substituting for y so
-1/2x + 5 = -2x + 3 and x = -4/3
and then we put this to get y in either equation
y = -2(-4/3) + 3
y = 17/3
So the equations work

abidemiokin abidemiokin · Answer 2 · 2021-11-12T14:40:23+01:00

The only solution to the system of equation is (4, 11)

Let the given linear equation be given as shown:

y = 2x + 3 and y = 4x - 5

Equate both expressions since they are both "y" values

2x + 3 = 4x - 5

Collect the like terms

2x - 4x = -5- 3

-2x = -8

x = 8/2

x = 4

Substitute x = 4 into any of the equation

y = 2x + 3

y = 2(4) + 3

y = 11

This shows that the only solution to the system of equation is (4, 11)

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