Question

What is the solution to the system of linear equations? 2x+4y=20 and 3x+2y=26​

Answer 1

Answer:x=8,y=1

Step-by-step explanation:

2x+4y=20

So, 4y=20-2x

So,2y=10-x

Now we can use this information to use in the second equation

3x+2y=26

3x+(10-x)=26

2x+10=26

2x=16

x=8

Now that we know that x=8, then we can solve for y.

2x+4y=20

2(8) +4y=20

16+4y=20

4y=4

y=1

Answer 2

Here is the process of how I did it:

Step 1:     Make this equation : 2x+4y = 20 equal x by isolating x and bring everything else on the right side of the equation

2x + (4y-4y) = 20 - 4y

2x = 20 - 4y

$\frac{2x}{2} = \frac{20 - 4y}{2}$

x = 10 - 2y

Step 2: In the other equation given (3x+2y=26​) every time you see an x replace it with the equation solved above (x = 10 - 2y). This will help you find the y

3x+2y=26​ ---> 3(10 - 2y)+2y=26​

10(3) - 2y(3) + 2y = 26

30 - 6y + 2y = 26

(30-30) - 4y = (26 - 30)

$\frac{-4y}{-4} =\frac{-4}{-4}$

y = 1

Step 3: In the equation you found in step 1 (x = 10 - 2y) plug 1 into all the y's so you can find x

x = 10 - 2y ---> x = 10 - 2(1)

x = 10 - 2

x = 8

Hope this helped!