Problem

Solve for ' $x$ ' and ' $y$ ' in the following diagram

Answer

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Answer

The solution is in the simplest form: \(\boxed{(2,3)}\)

Steps

Step 1 ：Multiply the first equation by 5 and the second equation by $-2$ to get:\[10x-15y=-25,\ -10x + 4y =-8.\]

Step 2 ：Add the two equations to get: \[-11y = -33\]

Step 3 ：Divide both sides by -11 to find the value of y: \[y = 3\]

Step 4 ：Substitute y=3 in the first original equation: \[2x - 9 = -5\]

Step 5 ：Add 9 to both sides to get: \[2x = 4\]

Step 6 ：Divide both sides by 2 to find the value of x: \[x = 2\]

Step 7 ：Check the solution in both original equations: \[2(2) - 3(3) = -5,\ 5(2) - 2(3) = 4.\]

Step 8 ：The solution is in the simplest form: \(\boxed{(2,3)}\)

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