Pierre found a new store where he hopes to save money on his supplies. He bought 4 brushes and 7
tubes of paint for $32. He has another order for 6
brushes and 8 tubes of paint that will cost $43.
What is the cost of one brush? What is the cost of
one tube of paint?

Your first equation is 4x + 7y= 32, the x’s representing the brushes and the y’s the tubes of paint. Our second equation is 6x+8y=43. What I did is I multiplied the first equation by 1.5 so that it turns into 6x+10.5y=48. Then I subtracted the second equation from the first, canceling out the x’s and leaving us with 2.5y=5. Then divided and got y=2. We then go back to any of the original equations and plug it in to get the x’s.
6x+8(2)=43. We get 6x+16=43. We subtract and are left with 6x=27 and then x=4.5. Then plug both of them in to a different equation to double check. You could also use substitution by isolating one of the variables in one equation and then plugging it in to the other one.