Skills › Math › 8th grade 🧩 8th grade math · Patterns & Algebra
Two equations at once The solution of a system is the point where the two lines cross. It makes both equations true. Read across to find x, then up or down to find y. Left of the y-axis and below the x-axis are negative.
Worked example
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
Answer: x = 1
The solution is where the two lines cross: the point (1, 2). The x-coordinate is 1 .
For grown-ups: Systems of two linear equations. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.
What this practises, for teachers Practices systems of two linear equations (8.EE.C.8). A printable sheet with its answer key, worked answers on the page, no accounts.
For your class
On the board with this skill:
Try three The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
Show the answer and how Answer: y = 5
The solution is where the two lines cross: the point (1, 5). The y-coordinate is 5 .
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
Show the answer and how Answer: x = 3
The solution is where the two lines cross: the point (3, 1). The x-coordinate is 3 .
The two lines cross at one point. Which ordered pair (x, y) is the solution of the system?
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
Show the answer and how Answer: (1, −2)
The solution of a system is the point where the lines cross. Here they cross at (1, −2). Check it in both equations. Answer: (1, −2) .
Name: ____________________ Date: ____________ Score: ____ / 12
Two equations at once (8th grade) The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines are the graphs of two equations, and they cross at one point.
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
The two lines cross at one point. Which ordered pair (x, y) is the solution of the system?
−6 −5 −4 −3 −2 −1 1 2 3 4 5 6 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 Blue line Red line
Answer key x = 4 x = 3 x = 3 x = 1 x = 2 y = 3 y = -2 y = 4 x = 1 y = 2 x = -1 (1, −3) More 8th grade skills: all 8th grade math skills , or every grade at math skills .
By Aaron , founder of Peabody. About Peabody
The problems, the worked answers and the sheet are drawn by Peabody's code from the same generators the game uses, with no AI, the same way every time. Peabody is a learning app, not an assessment.
Something wrong or out of date? Write to aaron@peabody.kids .