SOLVING TWO VARIABLE EQUATIONS Brittney

Methods ◦ Graphing ◦ Slope intercept y=mx+b ◦ Standard form Ax+By=C ◦ Substitution ◦ Solve for one variable then plug the found variable into the other equation ◦ Elimination ◦ Cancel one variable then plug the found into the other equation

Graphing ◦ Step one: put each equation in slope intercept form. (y=mx+b) ◦ 1) 4x+2y=6 ◦ 2) 2x+y=4 ◦ For Equation one, subtract 4x, so they equation would be 2y=-4x+6 ◦ Then divide equation one by two, to isolate y y=-2x+3 ◦ y=-2x+3 is the final equation ◦ Repeat the process for equation 2. ◦ Subtract 2x from both sides of the equation, so the equation would be y=2x+4 ◦ Since y is already isolated, you don’t have the divide by anything ◦ Graph y=-2x+3, and y =2x+4 ◦ Their intersection on the graph would be the equations solution ◦ Check the solution by plugging the (X,Y) back into equation one and two

Substitution ◦ Step one pick a variable to solve for, for example y ◦ -2x+y=4 ◦ 3x+y=9 ◦ Add -2x to 4 to isolate y, so the equation should be y=2x+4 ◦ Plug the equation 2x+4, where y should be into equation two ◦ The new equation should look like 3x+2x+4=9 ◦ Now add like terms, so combine 3x and 2x, then subtract 4 from 9 ◦ The equation should look like 5x=5 ◦ Divide both sides by 5 to isolate x ◦ X=1

Substitution continued ◦ Since x=1, plug 1 back into equation two, 3(1) + y =9 ◦ Solve for y ◦ Multiply 3  1, to get 3 then subtract 3 from 9 to get 6 ◦ (1,6) ◦ Check your answers by plugging your x and y back into equations ◦ -2(1)+6=43(1)+6=9 ◦ -2+6=4 3+6=9 ◦ 4=49=9

Elimination ◦ Pick a variable to cancel out, for example x ◦ X+3y=-5 ◦ 4x-y=6 ◦ To cancel x multiple equation one by -4, so the equation would look like, -4x-12y=20 ◦ Add the 2 equation to cancel the x’s out ◦ -4x-12y=20 ◦ 4x-y=6 ◦ The new equation should look like -13y=26 ◦ Divide both sides by -13 to isolate y ◦ The equation should look like y=-2

Elimination continued ◦ Since y=-2, plug the y back into equation two. ◦ 4x-(-2)=6 ◦ A negative times a negative would give you positive 2 ◦ Subtract the 2 from 6, to give you 4x=4 ◦ Divide both sides by 4 to isolate x ◦ The equation should be x=1 ◦ Now that you have your x and y, plug them into equation one and two to see if its true. ◦ (1,-2) ◦ 1+3(-2)=-5 4(1)-(-2)=6 ◦ 1-6=-5 4+2=6 -5=-5 6=6 ◦ They're both true, so the solution is correct

Links Elimination ◦ Substitution ◦ ◦ Graphing ◦