SAT Math · Advanced Math
Systems of equations in two variables practice questions
Each free question on this page comes with its answer and a full explanation, and each one is marked easy, medium or hard.
- Question 35 · hardFor what value of k is the line y = 2x + k tangent to the parabola y = x² - 4x + 7?
- Question 64 · hardA circle is defined by x² + y² = 25. A line given by y = x + 1 intersects the circle at two points, forming a chord. What is the…
- Question 96 · mediumIf x² + y = 10 and x² - y = 4, what is the value of y?
- Question 97 · mediumHow many real solutions does the system y = -x² + 4x + 1 and y = x - 2 have?
- Question 98 · mediumThe equations x² - 5x + 6 = 0 and x² + kx - 12 = 0 share x=3 as a common root. What is the value of k?
- Question 114 · hardThe circle x² + y² = 8 is tangent to the line y = x + k for a positive value of k. What is that value of k?
- Question 115 · mediumThe graphs of y = x² and y = 3x + 4 intersect at two points. What is the sum of the x-coordinates of these two points?
- Question 116 · mediumIf x + y = 8 and xy = 12, what is the value of x² + y²?
- Question 118 · mediumThe system x² + y² = 25 and y = x - 1 has two solutions. Which solution satisfies the additional constraint x > 0?
- Question 176 · mediumIf x² + y = 21 and x² - y = 11, what is the positive value of x?
- Question 177 · mediumThe equations x² - 4x - 5 = 0 and x² + kx - 15 = 0 share x = 5 as a common root. What is the value of k?
- Question 217 · mediumThe graphs of y = x² - 3 and y = 4x - 3 intersect at two points. What is the product of the x-coordinates of these two points?
- Question 237 · mediumIf x² + y = 13 and x² - y = 5, what is the product of the two possible values of x?
- Question 278 · mediumThe graphs of y = x² + 2 and y = 6x - 4 intersect at two points. What is the sum of the x-coordinates of these two points?