![]() Representing the system graphically, we have:Īs you can see, the lines cut each other at (15, −5). So, equation 1 has a slope of −1 3 and y-intercept 0.Įquation 2 has a slope of −1 2 and y-intercept of 5 2. ![]() Let’s rearrange and rewrite equation 1 in the form y = mx + c. The former is in the standard form and the latter is in the slope-intercept form. You can cross-check if your solution is right by substituting the x and y values in the equations.ġ = 1 ✔ Graphing Equations Using Slope and Y-Intercept and Solving: Case 2 The point of intersection of the two lines is (6, 1). Representing the equations graphically we have: Solve y = −x + 7 and y = 2x 3 − 3 graphically.īoth equations are in the slope-intercept form. Thus, the solution of the system of equations is (−2, 4). Now, the ordered pair that corresponds to the point of intersection of the equations is the required solution. So, we must move up 1 unit and right 1 unit and plot the other point.ĭrawing a line connecting the points, we have:Īs you can see, both the lines intersect at a point. ![]() Let’s graph the second equation in the similar manner, too. When we connect these two points drawing a line, we get the graph of the first equation. So, let’s move down 1 unit and right 1 unit and plot another point. So, let’s plot the point (0, 2) on the coordinate plane. To graph the first equation, we need to use the slope and y-intercept. The given equations are already in the form y = mx + b, where m is the slope and b is the y-intercept. Graphing Equations Using Slope and Y-Intercept and Solving: Case 1 Let’s explore solving systems of equations in each of the cases. Step 3: The ordered pair of the point where the two lines intersect is the required solution. Step 2: Graph the equations using the slope and y-intercept or using the x- and y-intercepts.Ĭase 1: If the equations are in the slope-intercept form, identify the slope and y-intercept and graph them.Ĭase 2: If one of the equations is in slope-intercept form, rewrite the other one too in that form and graph them.Ĭase 3: If both the equations are in other forms, find the x- and y-intercepts and graph them. Step 1: Analyze what form each equation of the system is in. Let’s look at the step-by-step process of solving a linear system by graphing. Solving a System of Equations by Graphing In this lesson, we’ll deal with graphing and solving systems of equations that have a unique solution. ✯ When both equations represent the same line, the system has infinitely many solutions. ✯ When the lines are parallel, the system has no solution. There are two situations, we must consider. Here, the system has a unique solution and that would be (−1, −1). You’re right! The point of intersection of the two lines is the solution of the system. What do you think would be the solution of the system? But, we need to look for a solution that satisfies both equations simultaneously. When we consider each line individually, every point on it is the solution of respective equation. When the equations are graphed on a grid, we’ll have: You might wonder how this would help solve a system of linear equations. When we graph a linear equation on a coordinate plane, we get a straight line. How Does Graphing Help Solve a System of Equations?
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