How do you solve $5x+y=15, 2x+y=12$ using substitution?

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Answer 1 · 2016-12-10T22:32:37

$x = 1$ and $y = 10$

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

$5x - 5x + y = 15 - 5x$

$0 + y = 15 - 5x$

$y = 15 - 5x$

Step 2) Substitute $15 - 5x$ for $y$ in the second equation and solve for $x$ :

$2x + (15 - 5x) = 12$

$2x + 15 - 5x = 12$

$2x + 15 - 15 - 5x = 12 - 15$

$2x - 5x + 0 = -3$

$(2 - 5)x = -3$

$-3x = -3$

$(-3x)/(-3) = (-3)/(-3)$

$(-3)/(-3)x = 1$

$1x = 1$

$x = 1$

Step 3) Substitute $1$ for $x$ in the solution to the first equation in Step 1) and calculate $y$ :

$y = 15 - 5*1$

$y = 15 - 5$

$y = 10$

How do you solve 5x+y=15, 2x+y=125x+y=15, 2x+y=12 using substitution?