Question

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

Answer 1

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

Answer 2

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 =
`(2)/(3)`

Now, plug that into the first equation.

2x + y = 7 Substitute
2(
`(2)/(3)`) + y = 7 Multiply

`(4)/(3)` + y = 7 Subtract
`(4)/(3)` from each side
y = 5
`(2)/(3)`

The answer to the system of equations is (
`(2)/(3)`, 5
`(2)/(3)`).