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CCSS.Math: , , ,

we're told to look at the coordinate grid above I put it on the side here identify one system of two lines that has a single solution then identify one system of two lines that does not have that does not have a solution so let's do the first part first so a single solution single single solution and they say identify one system but we can see here actually there's actually going to be two systems that have a single solution and we talk about a single solution we're talking about a single x and y value that will satisfy both equations in the system so if we look right here at the points of intersection this point right there that satisfies this equation y is equal to zero point 1 X plus 1 and it also satisfies the well this blue line but the graph that that line represents y is equal to 4x plus 10 so this dot right here that point represents the solution to both of these or I guess another way to think about it it represents a x and y value that satisfy both of these constraints so one system that has one solution is the system that has y is equal to 0.1 X plus one and then this blue line right here which is y is equal to 4x plus 10 now they only want us to identify one system of two lines it has a single solution we've already done that but just so you see it there's actually another system here so this is one system right here or another system would be the green line and this red line this point of intersection right here once again that represents an x and y value that satisfies both the equation y is equal to 0.1 X plus 1 so Y is equal to 0.1 X plus 1 and this point right here satisfies the equation y is equal to 4x minus 6 y is equal to 4x minus 6 so if you look at this system there's one solution because there's one point of intersection of these two equations or these two lines and this system also has one solution because it has one point of intersection now the second part of the problem they say identify one system of two lines that does not have a single solution or does not have a solution so no solution no solution so in order for there to be no solution that means that the two constraints don't overlap that there's no point that is common to both equations or there's no there's no pair of XY values that's common to both equations and that's the case of the two parallel lines here this blue line in this green line because they never intersect there is no coordinate on the coordinate plane that satisfies both equations so there's no X&Y that satisfy both so the second part of the question a system that has no solution is y is equal to 4x plus 10 and then the other one is y is equal to Y is equal to 4x minus 6 and notice they have the exact same slope they have the exact same slope and there are two different lines they have different intercepts so they never ever intersect and that's why they have no solutions