The solution to the simultaneous equations
$5 x + 4 y = 14 and 3 x - 4 y = 2$

Answer

Expert–verified

Hide Steps

Answer

$x = 2$ and $y = 1$

Steps

Step 1 ：Multiply the first equation by 3 and the second equation by 5 to make the coefficients of y equal: $15 x + 12 y = 42$ and $15 x - 20 y = 10$

Step 2 ：Subtract the second equation from the first to eliminate y: $32 y = 32$

Step 3 ：Divide by 32 to find the value of y: $y = 1$

Step 4 ：Substitute the value of y back into one of the original equations to find the value of x: $5 x + 4 (1) = 14$

Step 5 ：Solve for x: $5 x = 10$ and $x = 2$

Step 6 ： $x = 2$ and $y = 1$