Question

Without solving, match the system of linear equations on the left with the number of solutions on the right.

y=−x+4
y=2x+3

Answer 1

Explanation:

you can do these by just looking at the equations and comparing the slopes and the y intercepts.

first, put ur equations in y = mx + b form where m is ur slope and b is ur y intercept. Thankfully, these are already in that form.

second, find ur slopes....they will be in the m position

y = mx + b

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

slope = -1 slope = 2

third, find ur y intercepts....they will be in the b position

y = mx + b

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

y int = 4 y int = 3

fourth, compare the slopes and y int's of equation 1 and equation 2

here are some rules...

if the slope and the y int are different in each equation, then there is only 1 solution

if the slope and y int are the EXACTLY the same in the simplest form of each equation, there is infinite solutions

if the slopes are the same, but the y int's different, there is no solution

so ur 2 equations have different slopes and different y int's.....

therefore, there is only 1 solution <=====