Let x be the number of peanuts pounds and y be the number of almod pounds. Then, we can write

and

Then, we have 2 equations in 2 unknowns. By multipliying by -3 the secon equation, we have an equivalent system of equations:

so, by adding both equations, we get

which gives

Then, by substituting this result into the equation x+y=10, we obtain

which gives

Therefore, she needs 4 pounds of peanuts and 6 pound of almonds