4x+y=10.x+y=7

March 19, 2026Mathematics

ScanSolve AI Answer

March 19, 2026

Answer

x=1,\ y=6

Step 1: Label the given equations.

\begin{cases} 4x + y = 10 \\ x + y = 7 \end{cases}

Step 2: Subtract the second equation from the first to eliminate $y$ .

(4x + y) - (x + y) = 10 - 7

4x + y - x - y = 3

3x = 3

Step 3: Solve for $x$ .

x = \frac{3}{3} = 1

Step 4: Substitute $x = 1$ into the second equation to solve for $y$ .

1 + y = 7

y = 7 - 1 = 6

Step 5: Verify the solution in the first equation.

4(1) + 6 = 4 + 6 = 10

The solution is correct.

Final answer:
$\boxed{x=1,\ y=6}$

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