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24 votes
24 votes
which graph shows the solution of the system of equations?
4x - 3y = 15
y = (2)/(3) - 1

which graph shows the solution of the system of equations?4x - 3y = 15y = (2)/(3) - 1-example-1
User Itsho
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1 Answer

14 votes
14 votes

The graph must show both linear equations.

The solution is the intersection between the two lines.

In order to know which graph is correct, we will express the equations in the form:


y=mx+b

where m is the slope of the line and b is the y-intercept.

We start with:


\begin{gathered} 4x-3y=15 \\ -3y=-4x+15 \\ y=(4)/(3)x-5 \end{gathered}

The other equation becomes:


y=(2)/(3)x-1

We know that the bottom graphs can not be the ones because they have a line with negative slope, and both equations have positive slope.

Now we look at the y-intercept.

Both are negative, so we can discard the right chart.

The solution seems to be the first graph (top left).

We can check. We have a y-intercept at y=-1 and y=-5.

The slope can be checked too, looking at any point in the line and veryfing in the equation.

User Matt Kent
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3.1k points