From [math]x – y = 3[/math], rearrange to make x the subject: [math]y = x – 3[/math].

Substitute into [math]2x + y = 10[/math]

[math]2x + (x – 3) = 10[/math]

Simplify:

[math]3x – 3 = 10[/math]

[math]3x = 13[/math], so [math]x = \frac{13}{3}[/math]

Substitute [math]x[/math] into [math]y = x – 3[/math]

[math]y = \frac{13}{3} – 3 = \frac{4}{3}[/math]

Solution:

[math]x = \frac{13}{3}[/math], [math]y = \frac{4}{3}[/math]

You can check your answer by substituting into [math]2x + y = 10[/math]:

[math] 2\left(\frac{13}{3}\right) + \frac{4}{3} = \frac{26}{3} + \frac{4}{3} = \frac{30}{3} = 10 [/math]