solve the linear system by graphing. y=x+1   y=-3x+9?

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flbyrne's profile pic

flbyrne | (Level 3) Assistant Educator

Posted on

The point of intersection of the two lines is (2,3), therefore the solution is x=2, y=3

Verify by substituting 2 for x and 3 for y in y=x+1

`3=2+1`

`3=3`

Substitute 2 for x and 3 for y in y=-3x+9

`3=-(3)(2)+9`

`3=-6+9`

`3=3`

PrunTuns's profile pic

PrunTuns | (Level 1) Honors

Posted on

When solving a linear system such as this one (which consists of two lines), the solution is the point at which the two lines intersect. 

In order to graph either y=x+1 or y=-3x+9, you must determine its slope and its y-intercept. Slope-intercept form is y=mx+b. "m" is the slope, while "b" is the y-intercept.

In y=x+1, therefore, b=1, and m=1 (or 1/1). Graph the point (0,1), then from that point move up one and to the right one. 

Likewise, in y=-3x+9, b=9, and m=-3 (or -3/1). Graph the point (0,9), then from that point move down three and to the right. 

Draw your lines, and there should an intersection point at (2,3). 

 

 

 

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The equations y=x+1 and y=-3x+9 have to be solved by graphing.

Draw the graph of the two equations. The coordinates of the point of intersection of the two lines is the solution of the system of equations.

From the graph it can be seen clearly that the point of intersection is (2, 3). The solution of the given equations is x = 2 and y = 3

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