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-y = x so y = -x Replace y to -x in first equation. Now solve the first equation.
Not visual enough?
To solve a system of equations by substitution, solve one equation for one variable, and substitute in the other. Then solve the equation for one variable. Once you have that variable, substitute its value into one of the original equations to get the other variable. Since the second equation is solved for x, x = -y, where you see x in the first equiation, insert -y. y = 2x - 3 We know x = -y, so y = 2(-y) - 3 y = -2y - 3 3y = -3 y = -1 Now substitute -1 in for y in the first equation: y = 2x - 3 -1 = 2x - 3 2 = 2x 1 = x Solution: x = 1, y = -1
^ Solve systems by ADDITION...
You're so funny geerky42! XD
What's so funny about it? It worked.
To solve a system of equations by elimination, add the two equations together to eliminate one variable. If just adding the two equations together does not eliminate a variable, you need to multiply one or both equation by a factor, so that one variable will get eliminated. Here we have y = 2x - 3 -y = x If you notice, adding the two equations does eliminate y, since you have y in one equatuion and -y in the other and y and -y add up to zero. In this case there is no need to multiply either equation by a factor. y = 2x - 3 -y = x (add) -------------- 0 = 3x - 3 Add 3 to both sides: 3 = 3x Divide both sides by 3: 1 = x To eliminate x from the equations, multiply the second equation by -2, so you get -2x, which when added to 2x of the first equation will eliminate x. y = 2x - 3 -y = x, multiplied by -2 becomes 2y = -2x Rewrite first eq and the second equation multiplied by -2: y = 2x - 3 2y = -2x (add) ------------- 3y = -3 y = -1 Once again, solution: x = 1, y = -1
Yeah, thanks for the help.
BOTH of you.
Last step: check Use the values we got for x and y and insert in _both_ equations and make sure they satisfy in both equations. x = 1 and y = -1 Check first equation: y = 2x - 3 -1 =? 2(1) - 3 -1 = -1 Checks Check second equation: -y = x -(-1) =? 1 1 =1 Checks Since x and y works in both equations, it is the solution.