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Math  /  Algebra

Question2x+y=84x+3y=16\begin{array}{l}2 x+y=8 \\ 4 x+3 y=16\end{array}

Studdy Solution

STEP 1

1. We are given a system of two linear equations with two variables, x x and y y .
2. The goal is to find the values of x x and y y that satisfy both equations simultaneously.
3. We will use the method of substitution or elimination to solve the system.

STEP 2

1. Choose a method to solve the system (substitution or elimination).
2. Solve for one variable in terms of the other.
3. Substitute the expression into the other equation.
4. Solve for the remaining variable.
5. Substitute back to find the other variable.
6. Check the solution in both original equations.

STEP 3

We will use the method of elimination to solve the system.

STEP 4

Multiply the first equation by 3 to align the coefficients of y y for elimination:
3(2x+y)=3(8) 3(2x + y) = 3(8)
This gives us:
6x+3y=24 6x + 3y = 24

STEP 5

Subtract the second equation from the new equation obtained in Step 2:
(6x+3y)−(4x+3y)=24−16 (6x + 3y) - (4x + 3y) = 24 - 16
Simplify:
2x=8 2x = 8

STEP 6

Solve for x x :
x=82 x = \frac{8}{2}
x=4 x = 4

STEP 7

Substitute x=4 x = 4 back into the first original equation to find y y :
2(4)+y=8 2(4) + y = 8
8+y=8 8 + y = 8
y=8−8 y = 8 - 8
y=0 y = 0

STEP 8

Check the solution x=4 x = 4 , y=0 y = 0 in both original equations.
First equation:
2(4)+0=8 2(4) + 0 = 8
8=8 8 = 8 (True)
Second equation:
4(4)+3(0)=16 4(4) + 3(0) = 16
16=16 16 = 16 (True)
Both equations are satisfied.
The solution is:
x=4, y=0 x = 4, \, y = 0

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