Question

2x + y = 7 5x + y = 9 Solve the system of equations.

Answer 1

The first step of solving a system of equations is to solve one equation for a variable. I'll solve the first one for y.

2x + y = 7                     Subtract 2x from both sides
        y = -2x + 7

Now, plug that y value into the y of the second equation and solve for x.

            5x + y = 9          Substitute
5x + (-2x + 7) = 9          Adjust the signs to get rid of parentheses
    5x - 2x + 7 = 9          Combine like terms
           3x + 7 = 9          Subtract 7 from both sides
                 3x = 2          Divide both sides by 3
                   x = $\frac{2}{3}$

Now, plug that into the first equation.

2x + y = 7     Substitute
2($\frac{2}{3}$) + y = 7      Multiply
$\frac{4}{3}$ + y = 7     Subtract $\frac{4}{3}$ from each side
y = 5 $\frac{2}{3}$

The answer to the system of equations is ($\frac{2}{3}$, 5 $\frac{2}{3}$).

Answer 2

2x + y = 7
-                            Using elimination
5x + y = 9
__________
-3x + 0 = -2
__________

-3x = -2

x = -2/-3

x = 2/3

From 2x + y = 7,   substitute, x = 2/3

2*(2/3) + y = 7

4/3 + y = 7,    

y = 7 - 4/3

y = (21 - 4)/3 = 17/3

y = 17/3

x = 2/3,     and     y = 17/3