How do you solve the system $X+y=10$ and $5x-y=8$ ?

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Answer 1 · 2017-02-12T16:46:39

See the entire solution process below:

Step 1) Solve the first equation for $x$ :

$x + y = 10$

$x + y - color(red)(y) = 10 - color(red)(y)$

$x + 0 = 10 - y$

$x = 10 - y$

Step 2) Substitute $10 - y$ for $x$ in the second equation and solve for $y$ :

$5x - y = 8$ becomes:

$5(10 - y) - y = 8$

$(5 xx 10) - (5 xx y) - y = 8$

$50 - 5y - y = 8$

$50 - 6y = 8$

$-color(red)(50) + 50 - 6y = -color(red)(50) + 8$

$0 - 6y = -42$

$-6y = -42$

$(-6y)/color(red)(-6) = -42/color(red)(-6)$

$(color(red)(cancel(color(black)(-6)))y)/cancel(color(red)(-6)) = 7$

$y = 7$

Step 3) Substitute $-7$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$ :

$x = 10 - y$ becomes:

$x = 10 - 7$

$x = 3$

The solution is: $x = 3$ and $y = 7$ or $(3, 7)$

How do you solve the system X+y=10X+y=10 and 5x-y=85x-y=8?