So remember the transitive property here:
"If a = b and a = c, then b = c"
In this case, since y = -2x + 3 and y = -5x + 9, this means that -2x + 3 = -5x + 9. Substitute -5x + 9 into y of the first equation to solve for x:
[tex]-2x + 3 = -5x + 9[/tex]
Firstly, add 5x to both sides of the equation: [tex]3x + 3 = 9[/tex]
Next, subtract 3 on both sides: [tex]3x=6[/tex]
Lastly, divide both sides by 3 and your first answer will be [tex]x=2[/tex]
Next, since we have the value of x, substitute it into either equation to solve for y as such:
[tex]y=-2(2)+3\\y=-4+3\\y=-1\\\\y=-5(2)+9\\y=-10+9\\y=-1[/tex]
Putting it all together, your answer is (2,-1).
