Question

Solve the system 4x + 2y = 10 x = y + 13

Answer 1

Answer:  (6,-7)

Step-by-step explanation:

4x +2y = 10  

x = y + 13      Substitute the value of x into the first equation to solve for y.

4(y + 13) +2y = 10   apply the distributive property on the left side

4y + 52 + 2y = 10   Combine like terms on the left side

6y + 52 =  10    Subtract  52 from both sides

       -52     -52

6y = -42  

y= -7  

The value of y so input it into one of the equations to solve for x

4x + 2(-7) = 10  

4x - 14  =  10

       +14    +14

4x = 24

x= 6

Answer 2

Answer:

$x = 6$

$y = -7$

Step-by-step explanation:

We have the system of equations:

$4x+2y=10\\x=y+13$

Let's solve by substituting. We know that $x=y+13$, so we can substitute $y+13$ in as $x$ in the equation $4x+2y=10$.

$4(y+13) + 2y = 10$

Simplify this down so that we have $y$ on one side of the equation:

$4y + 52 + 2y = 10\\\\6y + 52 = 10\\\\6y = -42\\\\y = -7$

Now that we know the value of $y$, we can substitute it in to the equation $x = y+13$ to find $x$.

$x = -7+13\\\\x = 6$

Hope this helped!