5x+y=42 and 2x+y=30, find x and y

I know the answer is x=4 and y=22 but I don't know how to get them.
Thanks for any help.

Take any one of the equations. I'll pick 2x+y=30. Solve for y. y=-2x+30. Now substitute what y equals in that equation and plug it into the other. 5x+(-2x+30)=42. Simplify into 3x+30=42. Solve for x. 3x=12. Now x=4. Plug 4 into any equation. I'll pick 2x+y=30. You will get 2(4)+y=30....8+y=30....y=22

x=4
y=22

Solve for one of the y equations: 5x+y=42 ----> Y=42-5x (by subtracting 5x from both sides).

then insert it into second formula : 2x+42-5x=30 (note that the solved y in the first equation is the same as the y in the second.

2x+42-5x=30
now 2x-5x = -3x+42 =30 ( only add or subtract terms that both have x or y in them)
-3x=30-42 ( subtract 42 from both sides) ---> -3x=-12 x=4

now insert x which is 4 into y=42-5x ---> y= 42-5(4) so y = 22

Put the equations on top of each other like this
5x+y=42
2x+y=30
Make one equation negative so that you can eliminate one variable (y)
-5x-y+-42
2x+y=30
add the equations
-3x=-12
Divide
x=4
Now that you have one variable, plug it into one of the equations
5(4)+y=42
20+y=42
y=22

Solve for x or y in one of the equations. Doesn't really matter.

y=42-5x

Then plug into the y in the other equation...

2x + (42-5x)= 30

Then solve for x.

42-3x=30
-3x=-12
Divide by -3.

x=4

Then go back and plug in 4 for x into any of the equations.

2(4) + y=30

subtract 8

y=22

First, change all the signs on 2x+y=30, so it will equal -2x-y=-30. ( I did this so I can get rid of "y", to solve "x")
5x+y=42
-2x-y=-30
=
3x =12
x =4
Now, plug in "x", into any equation

5(4)+y=42
20+y=42
-20 -20
y=22

First isolate the y on one side
5x+y=42 and y=-2x+30
Substitute for y
5x+(-2x+30)=42
Simplify
3x+30=42
Iscolate x
3x=12
X=4

Plug x into the equation
5(4)+y=42
20+y=42
Isolate y
Y=22

(4,22)

5x + y = 42
==> y = 42 - 5x
2x+y = 30
==> y = 30 - 2x

so:
42 - 5x = 30 - 2x
==> 5x - 2x = 42 - 30
==> 3x = 12
==> x = 4
and so
y = 30 -2x
==> y = 30 -8
==> y = 22

Study how to solve systems of linear equations.

If you do not understand them, talk with your teacher.

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X =4
Y = 22