Systems of Two Equations: Ten Hard SAT Questions With Parallel Lines, Boat Speeds, and Age Traps

https://www.prepfriend.com PrepFriend.com is a free SAT practice site with a full curriculum and question practice for every topic in this video. Two lines walk into a test. Only one point gets both right, or no point at all. In this video from PrepFriend101, you get ten hard SAT questions on systems of two linear equations in two variables, solved slowly, with every trap named before it can catch you. What you will learn: how to spot a system with no solution by matching coefficient ratios, how to rewrite a system in slope form and compare slopes and intercepts, how to use a combination the question already gives you instead of solving everything, how to eliminate a variable by adding equations, how to set up age problems so every person shifts by the same number of years, and how to find a boat current from downstream and upstream speeds. Questions teased in this video: a no solution grid in question with coefficients three and four, a shortcut question where the second equation already gives the difference you need, a boat question with ninety six miles downstream and forty eight miles upstream, two slope matching questions where a constant letter controls whether the lines are parallel, an age question where a parent is twenty five years older than a child and the future sum is sixty five, a second no solution grid in question with a new multiplier, an elimination question where opposite y terms invite you to add, and two more boat current questions with smaller numbers that reward the same method. Trap warnings: do not stop at the multiplier when a parallel question asks for a coefficient, do not forget to multiply a given difference by three, do not pick the upstream speed or the boat speed when a boat question asks for the current, do not forget to halve the speed gap, do not copy an answer from a familiar looking question, do not shift only one person in an age problem, and do not pick a coefficient or a sum before dividing in an elimination question. Every Solve slide in this video shows all four choices with the correct answer highlighted and a trap name on every wrong choice, and every grid in Solve slide names the most likely wrong values with why each one is wrong. How to use this video: pause on every Ask slide, try the question yourself for sixty seconds, then watch the Solve slide and check your work back in both equations. If you miss one, replay the Solve slide and say the method out loud before moving on. That habit matters more than speed. Practice next: after this video, try the medium and easy systems sets on PrepFriend.com, then return for the substitution and elimination sets and the no solution and infinitely many solutions sets. Each set builds the same skills with different stories, so your method stays steady while the numbers change. Subscribe to PrepFriend101 for new SAT math sets every week, ring the bell so you never miss a set, and give a thumbs up if a trap in this video is one you have fallen for before. Comment with the question number that surprised you most, and tell us which method you want drilled next. Practice the full SAT curriculum and question practice at PrepFriend.com, and bring a friend who still thinks parallel lines eventually meet. They do not, and now you can prove it. Method guide for each shape in this set: for a no solution question, compare the ratios of the x coefficients, the y coefficients, and the constants, and remember that equal coefficient ratios with a different constant ratio mean parallel lines, while equal ratios all the way through mean the same line and infinitely many solutions. For a slope matching question, rewrite every equation in y equals m x plus b form before you compare anything, because a letter hiding in front of y changes both the slope and the intercept. For a combination question, read the question stem before you solve, because it may ask for three x minus three y or x plus y, and that combination may already appear in the given equations or appear after one addition. For an elimination question, look for opposite coefficients first, and if they are not opposites, multiply one equation by a small number to make them opposites before you add. For an age question, write the present ages first, then add the same number of years to every person, and only then set the sum equal to the given total. For a boat question, convert distances and times into speeds first, then add and subtract the downstream and upstream speeds to isolate the boat speed and the current speed separately, and always halve the gap for the current. #PrepFriend SAT math algebra systems of equations parallel lines elimination boat problems age problems SAT prep hard questions PrepFriend101 practice