Question

Find the values of x and y that make the equation true.

4 X
3x - 4
+
3 4y
y 8
7 25
- 2 4
The value of x that makes the equation true is
(Simplify your answer)

Answer 1

• x = -3
• y = 7

Explanation:

You want to solve the system of equations ...

• x +4y = 25
• 3x +y = -2

Solution

We can eliminate y by subtracting the first equation from 4 times the second:

4(3x +y) -(x +4y) = 4(-2) -(25)

11x = -33

x = -3

Using the second equation, we have ...

y = -2 -3x = -2 -3(-3) = 7

The values of x and y that make the equation true are ...

• x = -3
• y = 7

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Additional comment

The sum of matrices is the sum of corresponding terms. The constant terms on the diagonals are irrelevant to the values of x and y. The off-diagonal sums give the two equations solved here.

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