WHEN SOLVING A SYSTEM OF 2 EQUATIONS BY LINEAR COMB:

Say you have

3x+5y=12

x+4y=11 what you want to do is have either the x’s or y’s cancel. So on the bottom equation you will multiply it by -3 so that you get -3x. Don’t forget you must multiply the entire equation by -3!! So now you have:

3x+5y=12

-3x-12y=-33 Now you add the 2 equations. The x’s cancel out

-7y=-21 Divide by -7 to get y alone

y=3. To get x you must plug in y to one of the equations.

3x+5(3)=12 I substituted 3 for y

3x+15=12 subtract 15

3x=-3 divide by 3

x=-1

The solution to the system is (-1,3)

WHEN SOLVING A SYSTEM OF 2 EQUATIONS BY SUBS:

Say you have

8x+y=12

-2x+3y=10 You want to get y alone in 1 equation. Lets take the top one. Subtract 8x to get y alone. You now have:

y=-8x+12

-2x+3y=10 Plug in y to the 2nd equation.

-2x+3(-8x+12)=10 Use distributive prop.

-2x-24x+36=10 Simplify

-26x=-26 divide by -26

x=1 Plug in x to one of the equations.

8(1)+y=21

8+y=12 Subtract 8

y=4

The solution to this system is (1,4)

you will desire to isolate between the variables and plug it into one in all the different equations. Then repeat to get an equation with purely one variable. as an occasion, isolate ‘b’ in the 1st equation: b = (-a million/7)*(9a+30) then you definately can plug this expression into the 2d equation so: (-8/7)*(9a+30) +5c = 11. This equation is now in terms of ‘a’ and ‘c’ merely like the third. Isolate between the variables and replace to remedy. as an occasion, the third equation may well be arranged to examine: c = (a million/10)*(seventy 4+3a). in case you plug that ‘c’ into the recent 2d equation, you get: (-8/7)*(9a+30) +(a million/2)*(seventy 4+3a) = 11. remedy for ‘a’ and then lower back replace on your different variables.

just divide them