A pencil at a stationery store costs $1, and a pen costs $1.50. Stefan spent $7 at the store. He bought a total of 6 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? x + 1.5y = 7 x + y = 6 1.5x + y = 7 x = 6y x + 2y = 7 6x = 1.5y 2x + y = 7 6x = 1.5y Which statement is true about the solutions for the equation 5y + 8 = −2? It has no solution. It has one solution. It has two solutions. It has infinitely many solutions. What is the value of z for the equation 1/4z=-7/8+1/8z The incorrect work of a student to solve an equation 2(y + 6) = 4y is shown below: Step 1: 2(y + 6) = 4y Step 2: 2y + 8 = 4y Step 3: 2y = 8 Step 4: y = 4 Which of the following explains how to correct Step 2 and shows the correct value of y? Which statement is true for the equation 5n − 4 = 5n − 3? It has infinitely many solutions. It has two solutions. It has one solution. It has no solution. A system of two equations is shown below: Equation C: a = 2b + 7 Equation D: a = 5b − 3 What value of a can be substituted into equation D to solve the system of equations? 2b 5b 5b − 3 2b + 7 The incomplete work of a student to solve an equation is shown below: Step 1: 2x + 8 = 2 Step 2: ? Step 3: x = −6 ÷ 2 Step 4: x = −3 What is the missing Step 2? 2x = −6 2x = 6 2x = 10 2x = −10 Which set of steps shows the solution to the equation 3y = −9? y = −9 − 3; y = 6 y = −9 ÷ 3; y = −3 y = −9 ÷ (−3); y = 3 y = −9 − (−3); y = −6
What do you think is the correct one for the first one??
For the first problem, assign "x" and "y" to pencils and pens. (x=pencil, y=pen). You know you buy 6 items because it tells you. Therefore, the number x + y (pencils + pens) must be equal to 6. As for the other equation, this is dealing with price, so set the price of each item as the coefficient (the number you multiply each variable by). We are told that we spend $7, so therefore, the equation we choose should equal 7. Add the coefficient variables together and find it to be 7. The equation you should therefore see will resemble this. 1x + 1.5y = 7.
As for the second problem, simply solve by performing a function, but be sure to do so to both sides. That being said, 5y+8=-2 can be simplified by simply isolating 5y and subtracting 8 from both sides. This yields 5y = -10. Simplify for yourself from here, and use logic to determine how many solutions you can find.
For the incorrect student, remember the distributive property. Everything within the parenthesis must be multiplied by the "2" in front of it.
This should get you started, use similar logic and techniques to try the other problems. Ask specific questions in the future, don't just post your homework online.
I asked for it to be checked over no rude comments. but thank you.