Solve the system by substitution.EXAMPLESolve the system by substitution: Strategy We will...

Solve the system by substitution.

EXAMPLE

Solve the system by substitution:

Strategy We will use the substitution method. Since the system does not contain an equation solved for x or for y, we must choose an equation and solve it for x or y. It is easiest to solve for y in the first equation, because y has a coefficient of 1 in that equation.

WHY Solving 4x + y = 13 for x or solving −2x + 3y = −17 for x or for y would involve working with cumbersome fractions.

Solution

Step 1 We solve the first equation for y, because y has a coefficient of 1.

Step 2 We then substitute −4x + 13 for y in the second equation of the system. This step will eliminate the variable y from that equation. The result will be an equation containing only one variable, x.

Step 3 To find y, we substitute 4 for x in the substitution equation and simplify:

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Step 4 The solution is (4, −3). The graphs of the equations of the given system would intersect at the point (4, −3).

Step 5 To verify that this result satisfies both equations, we substitute 4 for x and −3 for y into the original equations of the system and simplify.

Check:

Since (4, −3) satisfies both equations of the system, it checks.