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 \(\frac{2}{3}\)).
