y = −x + 2
y = 3x + 1
Which description best describes the solution to the system of equations?
Line y = −x + 2 intersects line y = 3x + 1.
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
Line y = −x + 2 intersects the origin.
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Hey why don't you graph it?
|dw:1440143370187:dw| these are your x and y intercepts for your first equation connect the dots, also note that your equations are set up as y=mx+b format, which is equation of a line, where b is the y - intercept, and m is the slope.
To solve for y - intercept (it's given +2) but you set x = 0 and solve for y
To solve for x - intercept we set y = 0 and solve for x.
|dw:1440143797896:dw| This is y = -x+2, can you do the same with your second equation?
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any 2 lines that don't have the same slope will intersect somewhere
(if they DO have the same slope than they are parallel)
any equation that has an intercept =0 will pass through the origin - otherwise it will NOT
any line that has a slope = 0 will NOT intercept the x axis
any lint at has slope "infinity" (i.e. has the form x = constant) will NOTintercept the Y axis.
So you do not need to graph the lines - just look at the equations and the above facts and deduce the answer.
Good points, but I think you should still try to graph it out, if you're not sure and it's good practice!