I have to solve this equation using substitution.

3x+5y=10
2x+ 1/2y=24

This is all one problem

2 x + ( 1 / 2 ) y = 24 Multiply both sides by 10

20 x + ( 1 / 2 ) y * 10 = 24 * 10

20 x + 5 y = 240

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3 x + 5 y = 10

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20 x + 5 y = 240
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3 x - 20 x + 5 y - 5 y = 10 - 240

- 17 x = - 230 Divide both sides by - 17

- 17 x / - 17 = - 230 / - 17

x = 230 / 17

2 x + 1 / 2 y = 24

2 * 230 / 17 + ( 1 / 2 ) y = 24

460 / 17 + ( 1 / 2 ) y = 24 Subtract 460 / 17 to both sides

460 / 17 + ( 1 / 2 ) y - 460 / 17 = 24 - 460 / 17

( 1 / 2 ) y = 24 - 460 / 17

( 1 / 2 ) y = 24 * 17 / 17 - 460 / 17

( 1 / 2 ) y = 408 / 17 - 460 / 17

( 1 / 2 ) y = - 52 / 17 Multiply both sides by 2

y = - 104 / 17

Solutions :

x = 230 / 17 , y = - 104 / 17

using substitution:

multiply the 2nd by 2
4x + y = 48
y = 48-4x

sub into the 1st
3x + 5(48-4x) = 10
3x + 240 - 20x = 10
-17x = -230
x = 230/17
then y = 48-4(230/7) = -104/17

To solve the given system of equations using substitution, we will first solve one equation for one variable and substitute that expression into the other equation.

Let's start with the first equation and solve it for x:

3x + 5y = 10

Rearrange the equation to isolate x:

3x = 10 - 5y

Divide both sides of the equation by 3:

x = (10 - 5y) / 3

Now, substitute this expression for x into the second equation:

2x + (1/2)y = 24

Replace x with (10 - 5y) / 3:

2((10 - 5y) / 3) + (1/2)y = 24

To simplify the equation, distribute 2 to (10 - 5y):

(20 - 10y) / 3 + (1/2)y = 24

Next, we need to clear the fractions by multiplying every term by 6 to eliminate the denominators (3 and 2):

6((20 - 10y) / 3) + 6((1/2)y) = 6(24)

This simplifies to:

2(20 - 10y) + 3y = 144

Distribute 2 to (20 - 10y):

40 - 20y + 3y = 144

Combine like terms:

40 - 17y = 144

Now, isolate y by subtracting 40 from both sides:

-17y = 144 - 40

Simplify:

-17y = 104

Divide both sides by -17 to solve for y:

y = 104 / -17
y ≈ -6.12 (rounded to two decimal places)

Now that we have the value of y, substitute it back into the expression for x:

x = (10 - 5y) / 3

x = (10 - 5(-6.12)) / 3

Calculate:

x ≈ 11.04

So the solution to the system of equations is approximately x ≈ 11.04 and y ≈ -6.12.