Digital PSAT Math Practice Question 293: Answer and Explanation

Question: 293

Consider the following system of equations:

y - 4x = 5 and y - 13 = 2x

What is the y value at the point of intersection for these two equations?

Correct Answer: 21

Explanation:

21 These equations can quickly be solved for y. For the first, add 4x to both sides to get y = 4x + 5. In the second, add 13 to both sides: y = 2x + 13. Set the right sides of the equation equal to one another:

4x + 5 = 2x + 13

Get all of the x terms on the left by subtracting 2x from both sides, and get all of the constants on the right by subtracting 5 from both sides:

2x = 8

Dividing by 2 tells you that x = 4. However, the question asks for the y-value at which they intersect. Plug 4 in for x in either equation to solve for y:

y = 4(4) + 5 = 16 + 5 = 21

So the answer is 21. Alternatively, you could have solved each equation for x and set those equal to one another to directly solve for the y-coordinate of their intersection; you could have also used elimination to solve.