Question

3x+4y=48

6x+2y=60

solve with steps

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this system of equations:

Step 1: Multiply the first equation by 2 and the second equation by 4 to eliminate y:

2(3x + 4y) = 2(48)
4(6x + 2y) = 4(60)

This simplifies to:
6x + 8y = 96
24x + 8y = 240

Step 2: Subtract the first equation from the second equation to eliminate y:

(24x + 8y) - (6x + 8y) = 240 - 96

This simplifies to:
18x = 144

Step 3: Divide both sides of the equation by 18 to solve for x:

18x/18 = 144/18
x = 8

Step 4: Substitute the value of x (8) into one of the original equations, such as the first equation, to solve for y:

3(8) + 4y = 48
24 + 4y = 48

Step 5: Subtract 24 from both sides of the equation:

4y = 48 - 24
4y = 24

Step 6: Divide both sides of the equation by 4 to solve for y:

4y/4 = 24/4
y = 6

Therefore, the solution to the system of equations is x = 8 and y = 6.

Answer 2

[AI-generated answer — Explain Bot]

To solve this system of equations, you can use the method of substitution or elimination. Here, I'll explain the steps using the substitution method.

Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the first equation for x:
3x + 4y = 48

Rearranging the equation, we get:
3x = 48 - 4y

Dividing by 3, we find:
x = (48 - 4y) / 3

Step 2: Substitute the expression for x in the second equation.
Now, substitute the expression for x in the second equation:
6x + 2y = 60

Replace x with (48 - 4y) / 3:
6((48 - 4y) / 3) + 2y = 60

Step 3: Simplify and solve for y.
Start by simplifying the equation:
(6 * 48 - 6 * 4y) / 3 + 2y = 60

(288 - 24y) / 3 + 2y = 60

Multiply both sides by 3 to eliminate the fraction:
288 - 24y + 6y = 180

Combine like terms:
288 - 18y = 180

Subtract 288 from both sides:
-18y = 180 - 288

Simplify the right side of the equation:
-18y = -108

Divide both sides by -18:
y = -108 / -18

Simplify the right side:
y = 6

Step 4: Substitute the value of y back into one of the original equations to find x.
Let's substitute y = 6 into the first equation:
3x + 4(6) = 48

3x + 24 = 48

Subtract 24 from both sides:
3x = 48 - 24

Simplify the right side:
3x = 24

Divide both sides by 3:
x = 24 / 3

Simplify further:
x = 8

So, the solution to the system of equations is x = 8 and y = 6.

Answer 3

[AI-generated answer — Step-by-Step Bot]

To solve the system of equations step-by-step, we can use the method of substitution.

Step 1: Solve one equation for one variable in terms of the other variable.
Let's start with the first equation:

3x + 4y = 48

Solving for x, we subtract 4y from both sides:

3x = 48 - 4y

Dividing both sides by 3:

x = (48 - 4y) / 3

Step 2: Substitute the expression for x obtained in Step 1 into the second equation.
Substitute the expression (48 - 4y) / 3 for x in the second equation:

6x + 2y = 60

6((48 - 4y) / 3) + 2y = 60

Step 3: Simplify the equation obtained in Step 2 and solve for y.
Using the distributive property:

(6 * 48 - 6 * 4y) / 3 + 2y = 60

(288 - 24y) / 3 + 2y = 60

Multiply both sides of the equation by 3 to eliminate the fraction:

288 - 24y + 6y = 180

Combine like terms:

288 - 18y = 180

Subtract 288 from both sides:

-18y = 180 - 288

-18y = -108

Divide both sides by -18:

y = -108 / -18

Simplifying:

y = 6

Step 4: Substitute the value of y back into one of the original equations and solve for x.
Substitute y = 6 into the first equation:

3x + 4(6) = 48

3x + 24 = 48

Subtract 24 from both sides:

3x = 48 - 24

3x = 24

Divide both sides by 3:

x = 24 / 3

Simplifying:

x = 8

So, the solution to the system of equations is x = 8 and y = 6.