Question

Look at the first two systems of equations from the table

above.
y=2x-1
y=x+1
and
y = 4x +3
y=2x+3
Notice that in both systems the slopes are different.
However, in one of the systems, the y-intercepts of the
two equations are different, but in the other system, the y-
intercepts are the same. The table above states that both
of these systems has only one solution.

How is that possible?

Answer 1

Let -5x+y=-3 be the first equation, and 3x-8y=24 be the second. Let's manipulate the first equation by adding 5x to both side; resulting in y=-3+5x, or 5x-3. Now let's plug in 5x-3 for wherever y has been in the second formula. 3x-8(5x-3)=24. This is now pretty straightforward to solve for x. We distribute the 8 into (5x-3) and get 3x-40x-24=24. -48=27x. x=-48/27, x=-16/9.

Now let's plug in the x for either one of the equations to get y. 3(-16/9)+8y=24. -16/3+8y=24. 8y=24+16/3. 24y=72+16. 24y=88. y=88/24, y=11/3.

Explanation: