1. Solving Systems by Graphing
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By graphing the given equations, we can determine the solution to the system. This will be the point at which the lines intersect. To do this, we will need the equations to be in slope-intercept form to help us identify the slope, m, and y-intercept, b.
Let's rewrite each of the equations in the system in slope-intercept form, highlighting the m and b values.
| Given Equation | Slope-Intercept Form | Slope m | y-intercept b |
|---|---|---|---|
| y=x+7 | y=1x+ 7 | 1 | 7 |
| y=2x+1 | y=2x+ 1 | 2 | 1 |
To graph these equations, we will start by plotting their y-intercepts. Then, we will use the slope to determine another point that satisfies each equation, and connect the points with a line.
We can see that the lines intersect at exactly one point.
It appears that the lines intersect at (6,13). This is the solution to the system.
To check our answer, we will substitute the solution into the given equations. If the substitutions result in true statements, then we will know that we have found the correct answer.
| Given | Substitute (6,13) | Simplify |
|---|---|---|
| y=x+7 | 13? = 6+7 | 13=13 |
| y=2x+1 | 13? =2( 6)+1 | 13=13 |
Our solution is correct.