You are watching: How many solutions exist for the given equation

Click here to watch ALL difficulties on Linear-equationsConcern 142804: -Determine how many remedies exist-Use either elimicountry or substitution to uncover the options (if any)-Graph the two lines, labeling the x-intercepts, y-intercepts, and points of interarea x + y = 3 and y = x + 3 Answer by MathLover1(18852) (Show Source): You can put this solution on YOUR website! and ; you have the right to create them both in the conventional develop favor this: Solved by pluggable solver: Solving a straight mechanism of equations by subsitution Lets start via the given device of direct equations Now in order to deal with this system by using substitution, we need to settle (or isolate) one variable. I"m going to choose y. Solve for y for the initially equation Subtract from both sides Divide both sides by 1. Which breaks down and reduces to Now we"ve fully isolated y Because y equates to we have the right to substitute the expression right into y of the 2nd equation. This will get rid of y so we can solve for x. Replace y via . Because this eliminates y, we have the right to now fix for x. Distribute 1 to Multiply Reduce any fractions Subtract from both sides Combine the terms on the ideal side Now incorporate the terms on the left side. Multiply both sides by . This will certainly cancel out and also isolate x So once we multiply and also (and also simplify) we gain Now that we recognize that , lets substitute that in for x to fix for y Plug in into the 2nd equation Multiply Add to both sides Combine the terms on the right side Multiply both sides by . This will cancel out 1 on the left side. Multiply the terms on the ideal side Reduce So this is the other answer So our solution is and which deserve to additionally look like (,) Notice if we graph the equations (if you need help with graphing, check out this solver) we acquire graph of (red) and also (green) (hint: you might need to resolve for y to graph these) intersecting at the blue circle. and also we deserve to watch that the 2 equations intersect at (,). This verifies our answer. ----------------------------------------------------------------------------------------------- Check: Plug in (,) into the device of equations Let and also . Now plug those values right into the equation Plug in and also Multiply Add Reduce. Since this equation is true the solution functions. So the solution (,) satisfies Let and . Now plug those worths right into the equation Plug in and Multiply Add Reduce. Since this equation is true the solution functions.

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So the solution (,) satisfies Due to the fact that the solution (,) satisfies the device of equations this verifies our answer.