MATRIX EQUATION
[ 3x ] [ 10+2y ]
[ y ] = [ 5-x ] Solve for x.
To solve for x in the matrix equation, you need to isolate the expression with x on one side of the equation. Here's how you can solve it step by step:
Step 1: Write the matrix equation:
[ 3x ] [ 10 + 2y ]
[ y ] = [ 5 - x ]
Step 2: Expand the right-hand side of the equation:
[ 3x ] [ 10 + 2y ]
[ y ] = [ 5 - x ]
Step 3: Distribute the values inside the second matrix:
[ 3x ] [ 10 + 2y ]
[ y ] = [ 5 - x ]
[ 3x ] [ 10 + 2y ]
[ y ] = [ 5 - x ]
Step 4: Separate the equation into two equations by looking at the elements on each side of the equality sign:
Equation 1: 3x = 10 + 2y
Equation 2: y = 5 - x
Step 5: Solve Equation 2 for x:
y = 5 - x
To isolate x, let's bring -x to the left side by subtracting y from both sides:
y + x = 5
Now, rearrange the equation to have x on one side:
x = 5 - y
Step 6: Substitute the value of x from Equation 2 into Equation 1:
3x = 10 + 2y
Substitute the value of x:
3(5 - y) = 10 + 2y
Step 7: Distribute 3 to both terms inside the parentheses:
15 - 3y = 10 + 2y
Step 8: Arrange the like terms on one side of the equation:
2y + 3y = 15 - 10
Combine like terms:
5y = 5
Step 9: Solve for y by dividing both sides of the equation by 5:
y = 1
Step 10: Substitute the value of y back into Equation 2 to find x:
x = 5 - y
x = 5 - 1
x = 4
Therefore, the solution to the matrix equation is x = 4.