Find the Variables

Problem

[[y,4],[3,2*x]]−[[x+3,−3],[2,3*y+1]]=[[1,7],[1,−9]]

Solution

1. Subtract the matrices on the left side by subtracting corresponding elements.

[[y−(x+3),4−(−3)],[3−2,2*x−(3*y+1)]]=[[1,7],[1,−9]]

2. Simplify the resulting matrix on the left side.

[[y−x−3,7],[1,2*x−3*y−1]]=[[1,7],[1,−9]]

3. Set up a system of linear equations by equating the corresponding entries.

y−x−3=1

2*x−3*y−1=−9

4. Rearrange the equations into standard form.

y−x=4

−3*y+2*x=−8

5. Solve the first equation for y

y=x+4

6. Substitute the expression for y into the second equation.

−3*(x+4)+2*x=−8

7. Distribute and solve for x

−3*x−12+2*x=−8

−x−12=−8

−x=4

x=−4

8. Calculate the value of y using the value of x

y=−4+4

y=0

Final Answer

x=−4,y=0

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