IXL | Solve a system of equations in slope-intercept form

Solve.

y = x + 4

y = 2x + 9

(, )

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Learn with an example

question

Solve.

y = ^–7x + 3

y = ^–x − 3

(, )

key idea

To solve using substitution, follow these four steps:

Step 1: Isolate a variable.

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.

Step 4: State the solution.

solution

Use any method to solve the system of equations, such as substitution.

y = ^–7x + 3

y = ^–x − 3

Step 1: Isolate a variable.

The variable y is already isolated in the first equation.

Step 2: Plug the result of Step 1 into the other equation and solve for one variable.

Plug y = ^–7x + 3 into the other equation, y = ^–x − 3, and find the value of x.

^–x − 3

Plug in y = ^–7x + 3

^–7x + 3

^–x − 3

Plug in y = ^–7x + 3

Add x to both sides

^–6x + 3

^–3

Add x to both sides

Subtract 3 from both sides

^–6x

^–6

Subtract 3 from both sides

Divide both sides by ^–6

Step 3: Plug the result of Step 2 into one of the original equations and solve for the other variable.

Take the result of Step 2, x = 1, and plug it into one of the original equations, such as y = ^–7x + 3. Then find the value of y.

^–7x + 3

Plug in x = 1

^–7(1) + 3

Plug in x = 1

Multiply

^–7 + 3

Multiply

Add

^–4

Add

Step 4: State the solution.

Since x = 1 and y = ^–4, the solution is (1, ^–4).

Looking for more? Try these:

Lesson: Systems of equations

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M.12Solve equations with variables on both sides

GG.1Is (x, y) a solution to the system of equations?

Lesson: Systems of equations

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