Which statement is true about the equations –3x + 4y = 12 and x – y = 1?
2 answers:
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Answer:
The system has one solution, at a single point of intersection.
Step-by-step explanation:
I'm going to assume that g and y are the same thing here, on a normal xy-coordinate plane. If there is actually a third dimension, 'g', then I am probably wrong, and I apologize.
For a system of 2 linear equations, a 'solution' is a point of intersection for the two lines.
If the two lines are parallel, they will have no intersection. These two equations are in the form y = mx + b, where m is the slope. <u>If their slopes are the same, then the lines are parallel.</u> The first equation has a slope of 2. The second equation has a slope of 6. 2 ≠ 6, obviously. They are are <u>not </u>parallel, so there is <u>at least one</u> solution (intersection)
If two equations are 'equivalent', then they represent the same exact line and you cannot find a unique solution to the system because there is no single point where they intersect. They intersect at <u>all </u>points, so there are an infinite number of solutions. Two equations in the same format (like point-slope) will be equivalent if you see that one is just a multiple of the other. That is not the case here. They are not equivalent, so there are not an infinite number of solutions.
For the intersection of two lines in a plane, that intersection is no point, 1 point, or infinite points.
We have ruled out no point and we have ruled out infinite points.
There must be a solution of one point where the two lines intersect.
That would be consistent with answers B and E as shown in your Brainly question.
